Question

PLZZ HELP FAST
If a⁴.b^5 =1, then the value of log[base a] (a^5.b⁴) equals-
A. 4
B. 5
C. 8/5
D. 9/5

Answer 1

Answer is D(9/5). Problem done in attachment.

Answer 2

Hi friend, Harish here.

Here is your answer:

Given that;

$a^4 \times b^5 = 1$

To find;

$The\ value \ of\ log_a a^5 b^4$

Solution:

$a^4 \times b^5 = 1$

⇒ $b^5 = \frac{1}{a^4} = a^{-4}$

⇒ $b = a^{ \frac{-4}{5}}$

Then,

$log_a a^5 b^4 = log_a a^5 + log_a b^4$

⇒ $5log_aa + log_a a^{ \frac{-16}{5}}$

⇒ $5 + \frac{-16}{5} = \frac{25-16}{5} = \frac{9}{5}$
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Hope my answer is helpful to you.