Question

Solve for x:
${(6)}^{3x - 2} = {(36)}^{x + 2}$

(A) 3
(B) 4
(C) 5
(D) 6​

Answer 1

Step-by-step explanation:

The correct answer is option (D) 6.

The given exponential equation is as:

6^ (3x - 2) = 36^ (x + 2)

Write 36 in exponential form with a base of 6.

i.e.,

6^ (3x - 2) = (6²)^ (x + 2)

=> 6^ (3x - 2) = 6^ 2x + 4

Since the bases are the same, set the exponents equal.

3x - 2 = 2x + 4

=> 3x - 2x = 4 + 2

=> x = 6.

Answer 2

ANSWER:

Given:

• $6^{(3x-2)}=(36)^{(x+2)}$

To Find:

• Value of x

Solution:

We are given that,

$\implies6^{(3x-2)}=(36)^{(x+2)}$

We know that,

$\hookrightarrow 36=6^2$

So,

$\implies6^{(3x-2)}=6^{2^{(x+2)}}$

We know that,

$\hookrightarrow a^{x^y}=a^{xy}$

$\implies6^{(3x-2)}=6^{2(x+2)}$

$\implies6^{(3x-2)}=6^{(2x+4)}$

We know that, if,

$\hookrightarrow a^x=a^y$

Then,

$\hookrightarrow x=y$

So,

$\implies6^{(3x-2)}=6^{(2x+4)}$

$\implies3x-2=2x+4$

Transposing 2x to RHS,

$\implies3x-2x-2=4$

Transpsoing -2 to LHS,

$\implies x=4+2$

So,

$\implies\bf x=6$

Therefore, value of x is 6.