Question

USE LAWS OF EXPONENT TO FIND THE VALUE OF X
㏒ ₆₄ 8=X÷2

Answer 1

Answer:

x = 1

Step-by-step explanation:

FACTS TO KNOW BEFORE SOLVING :-

Lets say , there's an expression → $a = b^c$

In terms of logarithm , it can be written as → $\log_b a = c$

SOLUTION :-

$\log_{64}8 = \frac{x}{2}$

It can be also written as -

$64^{\frac{x}{2} }= 8$

In L.H.S. , 64 can be written as 8² and in R.H.S. , 8 can be written as 8¹. So,

$=> 8^{(\frac{x}{2} \times 2)} = 8^1$

$=> 8^x = 8^1$

According to the law of exponents , the bases are equal in L.H.S & R.H.S. .So, their exponents in L.H.S. & R.H.S. must be equal.

$=> x = 1$