Question

What is 2 (log Subscript 3 Baseline 8 + log Subscript 3 Baseline z) minus log Subscript 3 Baseline (3 Superscript 4 Baseline minus 7 squared) written as a single logarithm?

Answer 1

Correct option is B) $log_3(2z^2)$ .

Explanation:

We have the following equation : 2 (log Subscript 3 Baseline 8 + log Subscript 3 Baseline z) minus log Subscript 3 Baseline (3 Superscript 4 Baseline minus 7 squared) to solve :

$2(log_38 + log_3z)-( log_3(3^4-7^2))$

⇒ $2(log_38 + log_3z)-( log_3(3^4-7^2))$

⇒ $2(log_3(8z)) -( log_3(3^4-7^2))$               { $loga +logb = Log(ab)$ }

⇒ $log_3(8z)^2 -( log_3(3^4-7^2))$

⇒ $log_364z^2 -( log_3(81-49))$

⇒ $log_364z^2 -( log_3(32))$           { $loga -logb = log(\frac{a}{b})$

⇒ $log_3(\frac{64z^2}{32})$

⇒ $log_3(2z^2)$

Therefore , Correct option is B) $log_3(2z^2)$ .

Answer 2

Answer:

log$_{3}$2z^2

Explanation: