Question

very tricky maths ques

Answer 1

Hey 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:

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

⇒ $b^5 = \frac{1}{a^4} = a^{-4}$  

⇒ $b = a^{ \frac{-4}{5}}$  - (i)

Then,

[tex]log_a a^5 b^4 = log_a a^5 + log_a b^4 [/tex]

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

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