Find log₂₃ 29 in terms of M and N, if log 23 = M and log 29 = N.

Expand the given logarithmic expression and try to evaluate by using the properties of logarithms.

log [(100y⁴√(2 - y))/(3(y + 8)³)]

Find the value of f(log₄ (3 ln 4)) for the function given below.

f(x) = 4^x

Find x for the following equation.

5|lnx| - 25 = 0

Solve the logarithmic equation for x and provide an exact solution:

log₄ (x² - 225) - log₄ (x + 15) = 1

In the given expression, solve for x. Make use of logarithms with proper bases.
M = R ((a/b) +1)^xy

Draw the graph of the following function. $f\left(x\right)=\left(\frac18\right)^{-x}$