Question

If log x base 4 + log x base 2=6 then find x

Answer 1

Answer:

x = 16

Solution:

See in the attachment.

Formula Used:

See in the attachment.

Answer 2

The value of x is 16

Given:

㏒₄ x + ㏒₂ x = 6

To find:

The value of x

Solution:

As we know ㏒ₓ y = log x / log y

⇒ ㏒₄ x = ㏒ x / ㏒ 4  

⇒ ㏒₂ x = ㏒ x / ㏒ 2

Given that ㏒₄ x + ㏒₂ x = 6

⇒  ㏒ x /㏒ 4 + ㏒ x / ㏒ 2 = 6

⇒  ㏒ x / ㏒ 2² + ㏒ x / ㏒ 2 = 6

⇒  ㏒ x / 2 ㏒ 2 + ㏒ x / ㏒ 2 = 6

⇒  $\frac{log x + 2 log x}{2 log 2} = 6$

⇒ ㏒ x + 2 ㏒ x = 6(2 ㏒ 2)

⇒ 3 ㏒ x = 12 ㏒ 2

⇒  ㏒ x = 4 ㏒ 2  

⇒  ㏒ x = ㏒ 2⁴

⇒ x = 2⁴

⇒  x =  16

The value of x = 16

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