What is the answer to ln(5^x-1)=3 ?

The answer to ln(5^x-1)=3 is x=(ln(e^3+1))/(ln(5))

Solve for x: ln(5^x-1)=3

The solution is x=(ln(e^3+1))/(ln(5))

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ln (5^{x} - 1) = 3

x = \frac{ln ( e ^{3} + 1 )}{ln ( 5 )}

Decimal Notation

x = 1.89419 \dots

Solution steps

ln (5^{x} - 1) = 3

Rewrite the equation with

5^{x} = u

ln (u - 1) = 3

Solve

ln (u - 1) = 3 : u = e^{3} + 1

u = e^{3} + 1

Substitute back

u = 5^{x},

solve for

x

Solve

5^{x} = e^{3} + 1 : x = \frac{ln ( e ^{3} + 1 )}{ln ( 5 )}

x = \frac{ln ( e ^{3} + 1 )}{ln ( 5 )}

e^{3 x - 1} = 15

2 5^{2 x + 4} = 62 5^{2 x - 1}

0.8 = \frac{e ^{- 5 + 3 x}}{1 + e ^{- 5 + 3 x}}

2 (3 e^{- x} x^{2} - e^{- x} x^{3}) = 0

e^{x} - 3 e^{- x} - 4 = 0

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