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Lina20 [59]
4 years ago
9

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.
Mathematics
1 answer:
aev [14]4 years ago
3 0

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)].

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