College Algebra
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Using the properties of logarithms, expand the following logarithmic expression:
Work out y.
log5(y + 96) - log5y = 2
Expand using properties of logarithms: log [(√a)/(100b6)]
Condense the given equation to a single logarithm whose coefficient is 1, and evaluate without using a calculator if possible.
ln y + ln(y2 - 9) - ln 3 - ln(y + 3)
(1/2)[3ln(a + 16) - ln(3a) - ln (a2 - 64)]
(1/3)(log3 a + log3 b) - 8log3(a + b)
(1/4)(ln a + ln b)
Find log23 29 in terms of M and N, if log 23 = M and log 29 = N.
Verify if the given equation is true. Make the necessary changes to support the conclusion and amend the equation to make it true if the statement given is false.logb [(mn)3] = (logb m + logb n)3
Verify if the given equation is true. Make the necessary changes to support the conclusion and amend the equation to make it true if the statement given is false.logn (a3 + b4) = 3 logn a + 4 logn b
Verify if the given equation is true. Make the necessary changes to support the conclusion and amend the equation to make it true if the statement given is false.log13 169 / log13 13 = log13 169 - log13 13
Verify if the given equation is true. Make the necessary changes to support the conclusion and amend the equation to make it true if the statement given is false.log2 13 = 1/log13 2
Verify if the given equation is true. Make the necessary changes to support the conclusion and amend the equation to make it true if the statement given is false.log7 [11(2x + 3)] = log7 (11) + log7 (2x + 3)
Verify if the given equation is true. Make necessary changes to support the conclusion and amend the equation to make it true if the statement given is false.log5 [(7x - 2)/(2x2 + 5)] = log5 (7x - 2) - log5 (2x2 + 5)
Verify if the given equation is true. Make the necessary changes to support the conclusion and amend the equation to make it true if the statement given is false. log(8x + 13)/log(3x - 1) = log(8x + 13) - log(3x - 1)
Verify if the given equation is true. Make the necessary changes to support the conclusion and amend the equation to make it true if the statement given is false. log(2x + 7) - log(5x) = log(2x + 7)/log(5x)
2ln w + 9ln v - 4ln u
8ln(y + 1) - 5ln y
2ln c - (1/2)ln d
9ln a - 7ln b
Verify if the given equation is true. Make the necessary changes to support the conclusion and amend the equation to make it true if the statement given is false. ln(5x) + ln(8x) = ln(13x)
Verify if the given equation is true. Make necessary changes to support the conclusion and amend the equation to make it true if the statement given is false. ln(7x) + ln 13 = ln(91x)
Verify if the given equation is true. Make the necessary changes to support the conclusion and amend the equation to make it true if the statement given is false. ln(3x +5) = ln(3x) + ln 5
Verify if the given equation is true. Make the necessary changes to support the conclusion and amend the equation to make it true if the statement given is false.n2(log2 2n) = n3
Verify if the given equation is true. Make necessary changes to support the conclusion and amend the equation to make it true if the statement given is false.ln(81a4) = 4ln(3a)
4logxa + 7logxc
(1/6)ln(a3) + ln b
log y + 8log z
log5(1125) - log5(9)
Condense the given equation to a single logarithm whose coefficient is 1.
lny + ln33
Condense the given expression to a single logarithm whose coefficient is 1.
log 7 + log 9
Expand the given logarithmic expression and try to evaluate by using the properties of logarithms.
log [(100y4√(2 - y))/(3(y + 8)3)]
ln[(y5(√(y2 + 7))/(y + 3)6]
log2 √((a3b2)/18)
logd [(√(2a) b4)/c9]
log√(a/b)
log7 √(49y)
logx (a3b2/c7)
log9 (81/√(x - 9))
log7(∛(y)/343)
logf (a7b)
log 7√y
log M- 11
logay6
ln(e9/3)
log3(81/k)
log(y/10000)
log19(19/y)
log(100000000x)
log13 (13x)
log2 (18 × 5)
Verify if the given equation is true. Make the necessary changes to support the conclusion and amend the equation to make it true if the statement given is false.log5 (13x5) = 5 log5 (13x)
State the expression in terms of M and N, if M =logc 8 and N = logc 7.logc √(8/49)
State the expression in terms of M and N, if M =logc 8 and N = logc 7.logc 343
State the expression in terms of M and N, if M =logc 8 and N = logc 7.logc 8/7
Evaluate the given expression using common or natural logarithms and a calculator up to four decimals.
logπ 501
log0.4 21
log8 91.5
log7 31
Evaluate the following logarithm to three decimal places, using common logarithm properties. The use of a calculator is allowed wherever needed.
log515947
Write the following as a single logarithmic expression using the properties of logarithms a ln x - 1/2ln y
Write the following as a single logarithmic expression using the properties of logarithms. 1/3log x+ 2log y
Determine logarithms without using a calculator wherever possible, while expanding logarithmic expression using properties of logarithms
ln xex^2
Determine logarithms without using a calculator wherever possible, while expanding logarithmic expression using properties of logarithms log2 32x5
Rewrite the following logarithmic function using the properties of logarithms. Then, use the written function to graph it:
f(x) = log5 [25(x - 6)]
f(x) = log7 [343(x + 4)]
Using the change-of-base theorem, express log12 56 in terms of the natural logarithm, ln.
Which of the given pairs of consecutive integers has log3 121 in between?
Evaluate the following logarithmic expression. If it is appropriate to write the answer in decimal, round it to four decimal places:
log 1082
5(log 0.01)
log 71
log 0.0077
log (261 × 17)
log (652/264)
log 411 + log 47
log 619 - log 231
Write the given logarithmic expression in terms of p and q where p = ln x and q = ln y.
ln (x5∛y)
ln (x4/y7)
Find the value of f(ln 8) for the function given below.
f(x) = ex
Find the value of f(ln 32) for the function given below.
Find the value of f(ln e) for the function given below.
Find the value of f(log4 3) for the function given below.
f(x) = 4x
Find the value of f(log4 ln 16) for the function given below.
Find the value of f(log4 (3 ln 4)) for the function given below.
Find the value of f(35) for the function given below.
f(x) = log3 x
Find the value of f(3log3 3) for the function given below.
Find the value of f(33 log3 3) for the function given below.
Which of the following logarithmic expressions is equivalent to 3 ln(9x)? Note that x is greater than 0.
Which of the following logarithmic expressions is equivalent to ln(63x) - ln(7x)? Note that x is greater than 0.
Estimate the value of the logarithm using a calculator. Express the answer in four decimal places.
ln 168,000
log1/5 (3/11)
Evaluate the following expression. Approximate your answer to three significant figures, if necessary.
ln e7.8
ln (1/e19)
ln √(e4)
ln 39
ln 0.00059
ln (35 • 872)
ln (54/29)
ln(35) + ln(872)
ln(54) - ln(29)
ln(96) - ln(23)
Evaluate the following and approximate the answer to three significant figures using the change-of-base theorem.
log3(7)
log12(0.77)
log1/4(7)
log2π(3e)
log√11(25)
log√23(8)
Evaluate the given expression.
log 472.6
log 4.726
Evaluate the pH of concrete, if the hydronium ion concentration is 4.6 × 10 -14.
Evaluate the pH of the solution, if the hydronium ion concentration is 5.6 × 10 -8 mol/L.
Evaluate the pH of the Bleaching powder, if the hydronium ion concentration is 2.5 × 10 -12 mol/L.
Evaluate the hydronium ion concentration for Yoghurt using the given pH.
4.3
Evaluate the hydronium ion concentration for orange juice using the given pH.
3.7
Categorize the wetland area as a rich fen, a poor fen, or a bog using the provided hydronium concentration.
3.89 × 10 -5 mol/L
3.89 × 10 -3 mol/L
3.89 × 10 -7 mol/L
Graph the function using the change of base property.y = log19 x
Graph the function using the change of base property.
y = log5 (x +6)