What is the answer to 4|5^x-1|=5^x ?

The answer to 4|5^x-1|=5^x is x=(ln(4/5))/(ln(5)),x=(ln(4/3))/(ln(5))

Solve for x: 4|5^x-1|=5^x

The solution is x=(ln(4/5))/(ln(5)),x=(ln(4/3))/(ln(5))

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4 ∣ 5^{x} - 1 ∣ = 5^{x}

x = \frac{ln ( \frac{4}{5} )}{ln ( 5 )}, x = \frac{ln ( \frac{4}{3} )}{ln ( 5 )}

Decimal Notation

x = - 0.13864 \dots, x = 0.17874 \dots

Solution steps

4 ∣ 5^{x} - 1 ∣ = 5^{x}

Rewrite the equation with

5^{x} = u

4 ∣ u - 1 ∣ = u

Solve

4 ∣ u - 1 ∣ = u : u = \frac{4}{5} or u = \frac{4}{3}

u = \frac{4}{5}, u = \frac{4}{3}

Substitute back

u = 5^{x},

solve for

x

Solve

5^{x} = \frac{4}{5} : x = \frac{ln ( \frac{4}{5} )}{ln ( 5 )}

Solve

5^{x} = \frac{4}{3} : x = \frac{ln ( \frac{4}{3} )}{ln ( 5 )}

x = \frac{ln ( \frac{4}{5} )}{ln ( 5 )}, x = \frac{ln ( \frac{4}{3} )}{ln ( 5 )}

3^{2 x - 2} = 9

\frac{1}{49} = 34 3^{x}

3^{2 x} - 1 = 15

27 (3^{2 x}) - 12 (3^{x}) + 1 = 0

8^{x} = \frac{2 ^{32} - 4 ^{14}}{30}

What is the answer to 4|5^x-1|=5^x ?
The answer to 4|5^x-1|=5^x is x=(ln(4/5))/(ln(5)),x=(ln(4/3))/(ln(5))
Solve for x: 4|5^x-1|=5^x
The solution is x=(ln(4/5))/(ln(5)),x=(ln(4/3))/(ln(5))