Question

log x to the base 2 find the value of x​

Answer 1

Step-by-step explanation:

Brainly.in

What is your question?

sanya4220

29.05.2019

Math

Secondary School

+5 pts

Answered

If log x at base root 2 = a then find the value of log x at the base 2 root 2

2

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sivaprasath

sivaprasath

Answer:

log_{2\sqrt{2}} \ x = \frac{a}{3}

Step-by-step explanation:

Given :

log_{\sqrt{2}} \ x=a

Then,

find the value of :

log_{2\sqrt{2}} \ x

Solution :

We know that,

log_{a^n} \ b=\frac{1}{n}log_{a} \ b

Also,.

We know that,

2 × √2 = (√2)² × √2 = (√2)³

So,

⇒ log_{2\sqrt{2}} \ x=log_{(\sqrt{2})^3} \ x=\frac{1}{3}log_{\sqrt{2}} \ b=\frac{1}{3}(a) = \frac{a}{3}

∴ log_{2\sqrt{2}} \ x = \frac{a}{3}