What is the answer to 8*3^x=1 ?

The answer to 8*3^x=1 is x=-(3ln(2))/(ln(3))

The solution is x=-(3ln(2))/(ln(3))

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8*3^x=1

8 \cdot 3^{x} = 1

x = - \frac{3 ln ( 2 )}{ln ( 3 )}

Decimal Notation

x = - 1.89278 \dots

Solution steps

8 \cdot 3^{x} = 1

Divide both sides by

8

3^{x} = \frac{1}{8}

Apply exponent rules

x ln (3) = ln (\frac{1}{8})

Solve

x ln (3) = ln (\frac{1}{8}) : x = - \frac{3 ln ( 2 )}{ln ( 3 )}

x = - \frac{3 ln ( 2 )}{ln ( 3 )}

3 x^{3} e^{- 4 x} - 10 x^{2} e^{- 4 x} = 48 x e^{- 4 x}

3^{k} = 33

10 0^{x - 2} = 100 0^{x}

\frac{8 1 ^{x + 5}}{3 ^{7 x + 2}} = 3^{x - 2}

4 \times 5^{x + 1} - 5 = 35