CPM Homework Help : A2C Problem 11-147

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11-147.

Rewrite each equation as an equivalent equation using log₁₀. You do not need to find a numerical answer. These are sometimes known as change of base problems.

$\operatorname{log}_{2}\left(3\right) = x$
Step 1(a):
Write the equation in exponential form.
2^x = 3
Step 2(a):
Take the logarithm of base 10.
log₁₀(2^x) = log₁₀(3)
Step 3(a):
Use the Power Property of Logarithms and solve for x.
xlog₁₀(2) = log₁₀(3)
Answer (a):
$x= \frac{ \log_{10}(3) }{\log_{10}(2) }$

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

$\operatorname{log}_{7}\left(12\right) = x$
Hint (c):
Use the same process as in part (a).

$\operatorname{log}_{a}\left(b\right) = x$
Hint (d):
Use the same process as in part (a).

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