What is the answer to 5^x-24=(25)/(5^x) ?

The answer to 5^x-24=(25)/(5^x) is x=2

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5^x-24=(25)/(5^x)

5^{x} - 24 = \frac{25}{5 ^{x}}

x = 2

Solution steps

5^{x} - 24 = \frac{25}{5 ^{x}}

Apply exponent rules

5^{x} - 24 = 25 (5^{x})^{- 1}

Rewrite the equation with

5^{x} = u

u - 24 = 25 (u)^{- 1}

Solve

u - 24 = 25 u^{- 1} : u = 25, u = - 1

u = 25, u = - 1

Substitute back

u = 5^{x},

solve for

x

Solve

5^{x} = 25 : x = 2

Solve

5^{x} = - 1 :

No Solution for

x \in R

x = 2

Verify Solutions:

x = 2

True

The solution is

x = 2

4 (3^{2 x}) = e^{x}

3^{x + 2} = 3^{1 - x} - 26

3^{x} = 9

2^{n} + 3^{m} = a^{k}

3^{x} = 8

What is the answer to 5^x-24=(25)/(5^x) ?
The answer to 5^x-24=(25)/(5^x) is x=2
Solve for x: 5^x-24=(25)/(5^x)
The solution is x=2