CPM Homework Help : A2C Problem 10-155

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10-155.

Use the properties of logarithms to rewrite each expression as an equivalent one using only one logarithm.

$\operatorname{log}_{3}\left(5\right) + \operatorname{log}_{3}\left(m\right)$
Hint (a):
Remember the rule log_b(N) + log_b(M) = log_b(NM).
Answer (a):
log₃ (5m)

$\operatorname{log}_{6}\left(p\right) − \operatorname{log}_{6}\left(m\right)$
Hint (b):
$\text{Remember the rule log}_{b}(N) -\text{log}_{b}(M)=\text{log}_{b}\left(\frac{N}{M}\right).$
Answer (b):
$\text{log}_{6}\left(\frac{p}{m}\right)$

$\operatorname{log}_{2}\left(r\right) + 3\operatorname{log}_{6}\left(z\right)$
Hint (c):
Look closely at the bases.

$\operatorname{log}\left(90\right) + \operatorname{log}\left(4\right) − \operatorname{log}\left(36\right)$
Hint (d):
See part (a) and (b).
Answer (d):
$\operatorname{log}\left(10\right) = 1$

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