What is the answer to 5^{2x}=5^x+30 ?

The answer to 5^{2x}=5^x+30 is x=(ln(6))/(ln(5))

Solve for x: 5^{2x}=5^x+30

The solution is x=(ln(6))/(ln(5))

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5^{2 x} = 5^{x} + 30

x = \frac{ln ( 6 )}{ln ( 5 )}

Decimal Notation

x = 1.11328 \dots

Solution steps

5^{2 x} = 5^{x} + 30

Apply exponent rules

(5^{x})^{2} = 5^{x} + 30

Rewrite the equation with

5^{x} = u

(u)^{2} = u + 30

Solve

u^{2} = u + 30 : u = 6, u = - 5

u = 6, u = - 5

Substitute back

u = 5^{x},

solve for

x

Solve

5^{x} = 6 : x = \frac{ln ( 6 )}{ln ( 5 )}

Solve

5^{x} = - 5 :

No Solution for

x \in R

x = \frac{ln ( 6 )}{ln ( 5 )}

300 = 1500 - 1500 (0.9)^{t}

2 \cdot 7^{- 6 x} = 36

e^{2 x} - 1 = 0

a, e^{2 ab} = e^{a}

6^{x} = 0.2 5^{2 x - 1}

What is the answer to 5^{2x}=5^x+30 ?
The answer to 5^{2x}=5^x+30 is x=(ln(6))/(ln(5))
Solve for x: 5^{2x}=5^x+30
The solution is x=(ln(6))/(ln(5))