Question

What is the solution of (log4x − 6) 16 = 4? x = −2 x = 2 x = 3 x = 4

Answer 1

The solution of log(4x-6)16=4 is x = 2.

Answer 2

Option 2nd is correct

x =2

Explanation:

Using logarithmic rules:

if
`\log_a b = x`, then
`a^x = b`

Given the equation:

`\log_(4x-6) 16 = 4`

Apply the rules we have;

`16 = (4x-6)^4`

We can write 16 as:

`16 = 2 \cdot 2 \cdot 2 \cdot 2 = 2^4`

then;

`2^4 = (4x-6)^4`

On comparing both sides we have;

`2 = 4x-6`

Add 6 to both sides we have;

`8 = 4x`

Divide by 4 to both sides we have;

2 = x

or

x = 2

Therefore, the value of x is, 2