What is the answer to 5^x-1/(5^{x-2)}=24 ?

The answer to 5^x-1/(5^{x-2)}=24 is x=2

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5^x-1/(5^{x-2)}=24

5^{x} - \frac{1}{5 ^{x - 2}} = 24

x = 2

Solution steps

5^{x} - \frac{1}{5 ^{x - 2}} = 24

Apply exponent rules

5^{x} - (5^{x})^{- 1} \cdot 5^{2} = 24

Rewrite the equation with

5^{x} = u

u - (u)^{- 1} \cdot 5^{2} = 24

Solve

u - u^{- 1} \cdot 5^{2} = 24 : 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

1 0^{6 x} = 3^{3 x + 4}

6^{x} = 60

6^{x} = 18

3^{2 n - 2} = 9

0. 1^{11 - x} = 1 0^{2 x - 5}

What is the answer to 5^x-1/(5^{x-2)}=24 ?
The answer to 5^x-1/(5^{x-2)}=24 is x=2
Solve for x: 5^x-1/(5^{x-2)}=24
The solution is x=2