What is the answer to ln(3^x)=-1 ?

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

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ln(3^x)=-1

ln (3^{x}) = - 1

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

Decimal Notation

x = - 0.91023 \dots

Solution steps

ln (3^{x}) = - 1

Rewrite the equation with

3^{x} = u

ln (u) = - 1

Solve

ln (u) = - 1 : u = \frac{1}{e}

u = \frac{1}{e}

Substitute back

u = 3^{x},

solve for

x

Solve

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

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

49 \cdot 7^{3 x} = 5^{x}

4^{x + 3} + 4^{x} = 260

8^{x + 2} = 4

2^{x + 1} + 2^{x - 1} + 2^{x} = 28

2 5^{x} + 5^{1 + 2 x} = 20