In Exercises 60–63, determine whether each equation is true or fa...

Question

In Exercises 60–63, determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement. (log2 x)^4 = 4 log2 x

Accepted Answer

Hello. Today we're going to be determining whether a logarithmic equation is true or false. So the equation given to us is the logo rhythm of base five of X cubed is equal to three times log base five of X. Well in order to determine whether this is true or false, let's go ahead and recall the exponential rule for logarithms. So that rule states that if you have a logarithms of any base a with an argument x rays to any exponent, you're allowed to bring this exponent to the front of the logarithms as a product. Thus this could be rewritten as n times the logarithm of A. Of X. Now when we're looking on the left hand side of this equation Notice that the exponents is outside of this entire logarithms and not inside the argument. That means that we are not allowed to rewrite this as three times log base five of X. So it's not true. But in order for this to be true, this should have been written as log base five of X cubed that way. If the three was inside the argument it can be rewritten as three times the log base five of X. So the answer to this problem is going to be be the statement is not true and the left hand side of the equation should have been written as log base five of X cubed. So I hope this video helps you in determining whether this is true or false and I'll go ahead and see you all in the next video

In Exercises 60–63, determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement. (log2 x)^4 = 4 log2 x

Key Concepts

Properties of Logarithms

Exponential and Logarithmic Equivalence

Equation Verification

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