Question

Expand the following logs: 1" title="log_{2} \sqrt{ab^{3} }" alt="log_{2} \sqrt{ab^{3} }" align="absmiddle" class="latex-formula">

SHOW ALL WORK.

Answer 1

Answer:

$\log_2(ab^3)^{\frac{1}{2}}=\frac{1}{2}[\log_2(a)+3\log_2(b)]$.

Step-by-step explanation:

The given logarithmic expression is $\log_2\sqrt{ab^3}$.

We rewrite the radical as an exponent to obtain;

$\log_2(ab^3)^{\frac{1}{2}}$.

Recall that; $\log_a(M^n)=n\log_a(M)$

We apply this rule to obtain;

$=\frac{1}{2}\log_2(ab^3)$.

We now use the rule: $\log_a(MN)=\log_a(M)+\log_a(N)$

This implies that;

$=\frac{1}{2}[\log_2(a)+\log_2(b^3)]$.

We again apply: $\log_a(M^n)=n\log_a(M)$

$=\frac{1}{2}[\log_2(a)+3\log_2(b)]$.