Question

Expand the following logs:


`log_(2) \sqrt{ab^(3) }`

SHOW ALL WORK.

Answer 1

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

Explanation:

The given logarithmic expression is
`\log_2√(ab^3)`.

We rewrite the radical as an exponent to obtain;

`\log_2(ab^3)^{(1)/(2)}`.

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

We apply this rule to obtain;

`=(1)/(2)\log_2(ab^3)`.

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

This implies that;

`=(1)/(2)[\log_2(a)+\log_2(b^3)]`.

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

`=(1)/(2)[\log_2(a)+3\log_2(b)]`.