Question

1. solve the following exponential equation without using logarithms.

$2^{5x - 7}=4$
the solution is $x = \square$.
(type an integer or a simplified fraction. use a comma to separate answers as needed.)

Explanation:

Step1: Express 4 as power of 2

$4 = 2^2$

Step2: Set exponents equal (same base)

$5x - 7 = 2$

Step3: Solve for x (add 7 to both sides)

$5x = 2 + 7 = 9$

Step4: Isolate x (divide by 5)

$x = \frac{9}{5}$

Answer:

$\frac{9}{5}$