Question

$7^{(x +2) }=49^{(2x-3)} , x=\rule{1cm}{ 0 .1 pt}$

• A. 5
• B. 8/3
• C. 5/3
• D. 3

Answer 1

Answer:

B. 8/3

To find the value of $x$ in the equation $7^{(x+2)} = 49^{(2x-3)}$, follow these steps:

1. Equate the Bases

Since $49$ is $7^2$, rewrite the equation using the same base:
$7^{(x+2)} = (7^2)^{(2x-3)}$

2. Simplify the Exponents

Apply the power rule $(a^m)^n = a^{m \cdot n}$ to the right side:
$7^{(x+2)} = 7^{2(2x-3)}$

$7^{(x+2)} = 7^{(4x-6)}$

3. Solve for $x$

Since the bases are equal, the exponents must be equal:
$x + 2 = 4x - 6$

Rearrange the terms:
$2 + 6 = 4x - x$

$8 = 3x$

Answer: $x = \mathbf{\frac{8}{3}}$ (or approximately 2.67).