What is the answer to 5^{x+1}+6*5^x=6 ?

The answer to 5^{x+1}+6*5^x=6 is x=(ln(6/11))/(ln(5))

Solve for x: 5^{x+1}+6*5^x=6

The solution is x=(ln(6/11))/(ln(5))

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5^{x + 1} + 6 \cdot 5^{x} = 6

x = \frac{ln ( \frac{6}{11} )}{ln ( 5 )}

Decimal Notation

x = - 0.37661 \dots

Solution steps

5^{x + 1} + 6 \cdot 5^{x} = 6

Factor

5^{x + 1} + 6 \cdot 5^{x} : 11 \cdot 5^{x}

11 \cdot 5^{x} = 6

Divide both sides by

11

5^{x} = \frac{6}{11}

Apply exponent rules

x ln (5) = ln (\frac{6}{11})

Solve

x ln (5) = ln (\frac{6}{11}) : x = \frac{ln ( \frac{6}{11} )}{ln ( 5 )}

x = \frac{ln ( \frac{6}{11} )}{ln ( 5 )}

2^{2 x} = 31

1.0 6^{x} = 4.1

4^{x} = 8^{x - 2}

2^{2 x} = 11

e^{2 x} = 1.5 (2) + x

What is the answer to 5^{x+1}+6*5^x=6 ?
The answer to 5^{x+1}+6*5^x=6 is x=(ln(6/11))/(ln(5))
Solve for x: 5^{x+1}+6*5^x=6
The solution is x=(ln(6/11))/(ln(5))