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Popular >

a^{x+1}-a^x=1

Solution

a^{x + 1} - a^{x} = 1

Solution

x = - \frac{ln ( a - 1 )}{ln ( a )}

Solution steps

a^{x + 1} - a^{x} = 1

Factor

a^{x + 1} - a^{x} : a^{x} (a - 1)

a^{x} (a - 1) = 1

Divide both sides by

a - 1

a^{x} = \frac{1}{a - 1}

Apply exponent rules

x ln (a) = ln (\frac{1}{a - 1})

Solve

x ln (a) = ln (\frac{1}{a - 1}) : x = - \frac{ln ( a - 1 )}{ln ( a )}

x = - \frac{ln ( a - 1 )}{ln ( a )}

Popular Examples

4^x-9\times 2^x+8=0

4^{x} - 9 \times 2^{x} + 8 = 0

solvefor x,5^{2x-3}=3^{3x+4}solve for

x, 5^{2 x - 3} = 3^{3 x + 4}

125^{2x+3}=5^{x+4}

12 5^{2 x + 3} = 5^{x + 4}

ln (e^{x} - 1) = 1

9^{x-4}=3^{x+3}

9^{x - 4} = 3^{x + 3}

Frequently Asked Questions (FAQ)

What is the answer to a^{x+1}-a^x=1 ?
The answer to a^{x+1}-a^x=1 is x=-(ln(a-1))/(ln(a))