What is the answer to solvefor x,10^{x+1}-10^x=3 ?

The answer to solvefor x,10^{x+1}-10^x=3 is x=-(ln(3))/(ln(10))

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solvefor x,10^{x+1}-10^x=3

solve for

x, 1 0^{x + 1} - 1 0^{x} = 3

x = - \frac{ln ( 3 )}{ln ( 10 )}

Decimal Notation

x = - 0.47712 \dots

Solution steps

1 0^{x + 1} - 1 0^{x} = 3

Factor

1 0^{x + 1} - 1 0^{x} : 9 \cdot 1 0^{x}

9 \cdot 1 0^{x} = 3

Divide both sides by

9

1 0^{x} = \frac{1}{3}

Apply exponent rules

x ln (10) = ln (\frac{1}{3})

Solve

x ln (10) = ln (\frac{1}{3}) : x = - \frac{ln ( 3 )}{ln ( 10 )}

x = - \frac{ln ( 3 )}{ln ( 10 )}

\frac{2 ^{x} + 2 ^{- x}}{2} = 3

y, 3^{x} + 5^{y} = x^{3} + y

3^{2 x + 1} = 7^{x - 2}

2 e^{5 x + 2} = 17

2^{x} \cdot 5 = 1 0^{x}

What is the answer to solvefor x,10^{x+1}-10^x=3 ?
The answer to solvefor x,10^{x+1}-10^x=3 is x=-(ln(3))/(ln(10))