What is the answer to 25^x=5^x+6 ?

The answer to 25^x=5^x+6 is x=(ln(3))/(ln(5))

Solve for x: 25^x=5^x+6

The solution is x=(ln(3))/(ln(5))

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2 5^{x} = 5^{x} + 6

x = \frac{ln ( 3 )}{ln ( 5 )}

Decimal Notation

x = 0.68260 \dots

Solution steps

2 5^{x} = 5^{x} + 6

Apply exponent rules

(5^{x})^{2} = 5^{x} + 6

Rewrite the equation with

5^{x} = u

(u)^{2} = u + 6

Solve

u^{2} = u + 6 : u = 3, u = - 2

u = 3, u = - 2

Substitute back

u = 5^{x},

solve for

x

Solve

5^{x} = 3 : x = \frac{ln ( 3 )}{ln ( 5 )}

Solve

5^{x} = - 2 :

No Solution for

x \in R

x = \frac{ln ( 3 )}{ln ( 5 )}

5^{x - 3} = 2 5^{x - 5}

2^{x} = \frac{1}{8}

3000 (1 + 0.2)^{n} = 10000

3^{3 + x} = 7

- 2 = \frac{2 π}{( e ^{- c} + 1 )}

What is the answer to 25^x=5^x+6 ?
The answer to 25^x=5^x+6 is x=(ln(3))/(ln(5))
Solve for x: 25^x=5^x+6
The solution is x=(ln(3))/(ln(5))