What is the answer to 5^{x-1}=5^x-5 ?

The answer to 5^{x-1}=5^x-5 is x=(ln(5/4))/(ln(5))+1

Solve for x: 5^{x-1}=5^x-5

The solution is x=(ln(5/4))/(ln(5))+1

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5^{x - 1} = 5^{x} - 5

x = \frac{ln ( \frac{5}{4} )}{ln ( 5 )} + 1

Decimal Notation

x = 1.13864 \dots

Solution steps

5^{x - 1} = 5^{x} - 5

Subtract

5^{x}

from both sides

5^{x - 1} - 5^{x} = 5^{x} - 5 - 5^{x}

Simplify

5^{x - 1} - 5^{x} = - 5

Factor

5^{x - 1} - 5^{x} : - 4 \cdot 5^{x - 1}

- 4 \cdot 5^{x - 1} = - 5

Divide both sides by

- 4

5^{x - 1} = \frac{5}{4}

Apply exponent rules

(x - 1) ln (5) = ln (\frac{5}{4})

Solve

(x - 1) ln (5) = ln (\frac{5}{4}) : x = \frac{ln ( \frac{5}{4} )}{ln ( 5 )} + 1

x = \frac{ln ( \frac{5}{4} )}{ln ( 5 )} + 1

(\frac{1}{2})^{x} = \frac{1}{32}

2 7^{x} = 9^{x - 2}

3^{x} = 60

4^{x^{2} - 6 x} = 16384

4^{x^{2}} = 2^{x}

What is the answer to 5^{x-1}=5^x-5 ?
The answer to 5^{x-1}=5^x-5 is x=(ln(5/4))/(ln(5))+1
Solve for x: 5^{x-1}=5^x-5
The solution is x=(ln(5/4))/(ln(5))+1