Question

Solve the exponential equaion for x.


5^7x+5 = 125^2x-7

Answer 1

The answer would be x= -3/15625 (It’s a fraction)

Answer 2

To solve the exponential equation, recognize that 125 is a power of 5 and use this to rewrite the equation with a common base. Then, equate the exponents and solve for x, resulting in x = -26.

Solving the Exponential Equation

To solve the exponential equation for x:

5^(7x+5) = 125^(2x-7),

First, recognize that 125 is a power of 5, specifically 125 = 5^3. Thus, we can rewrite the equation using the same base:

• 5^(7x+5) = (5^3)^(2x-7)

According to the property of exponents, when raising a power to a power, we multiply the exponents. So the equation becomes:

• 5^(7x+5) = 5^(3(2x-7))

With the bases now the same, we can equate the exponents:

• 7x+5 = 3(2x-7)

Expanding the right side gives:

• 7x + 5 = 6x - 21

Subtract 6x from both sides:

• x + 5 = -21

Finally, subtract 5 from both sides to solve for x:

• x=-26