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

The answer to 3^{x+1}-10(3^x)=-3 is x=(ln(3/7))/(ln(3))

Solve for x: 3^{x+1}-10(3^x)=-3

The solution is x=(ln(3/7))/(ln(3))

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3^{x + 1} - 10 (3^{x}) = - 3

x = \frac{ln ( \frac{3}{7} )}{ln ( 3 )}

Decimal Notation

x = - 0.77124 \dots

Solution steps

3^{x + 1} - 10 (3^{x}) = - 3

Factor

3^{x + 1} - 10 \cdot 3^{x} : - 7 \cdot 3^{x}

- 7 \cdot 3^{x} = - 3

Divide both sides by

- 7

3^{x} = \frac{3}{7}

Apply exponent rules

x ln (3) = ln (\frac{3}{7})

Solve

x ln (3) = ln (\frac{3}{7}) : x = \frac{ln ( \frac{3}{7} )}{ln ( 3 )}

x = \frac{ln ( \frac{3}{7} )}{ln ( 3 )}

\frac{3}{2} = 1^{x}

5^{x + 3} = (\frac{( 1 )}{( 125 )})^{x}

e^{x} \cdot e^{- x} = 1

3^{x} + 3^{- x + 3} = 12

3^{2 x + 1} - 3^{x + 2} + 6 = 0

What is the answer to 3^{x+1}-10(3^x)=-3 ?
The answer to 3^{x+1}-10(3^x)=-3 is x=(ln(3/7))/(ln(3))
Solve for x: 3^{x+1}-10(3^x)=-3
The solution is x=(ln(3/7))/(ln(3))