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

Answer:

Option 2nd is correct

x =2

Step-by-step 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