CPM Homework Help : CCA2 Problem 11-59

Rewrite each equation as an equivalent equation using log_{$_{10}$}. You do not need to find a numerical answer. These are sometimes known as change of base problems.

log_{$_2$} $(3) = x$
Step 1(a):
Write the equation in exponential form.
$2^x = 3$
Step 2(a):
Take the logarithm of base $10$ .
log_{$_{10}$} $(2^x) =$ log_{$_{10}$} $(3)$
Step 3(a):
Use the Power Property of Logarithms and solve for $x$ .
xlog_{$_{10}$} $(2) =$ log_{$_{10}$} $(3)$
Answer (a):
$x= \frac{ \log_{10}(3) }{\log_{10}(2) }$

log_{$_5$} $(8) = x$
Hint (b):
Use the same process as in part (a).
Answer (b):
$x= \frac{ \log_{10}(8) }{ \log_{10}(5)}$

log_{$_7$} $(12) = x$
Hint (c):
Use the same process as in part (a).

log_{$_a$} $(b) = x$
Hint (d):
Use the same process as in part (a).