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

The answer to (3^x)^{x-1}=1 is x=1,x=0

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

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

x = 1, x = 0

Solution steps

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

Apply exponent rules

(x - 1) ln (3^{x}) = ln (1)

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or ln (3^{x}) = 0

Solve

x - 1 = 0 : x = 1

Solve

ln (3^{x}) = 0 : x = 0

x = 1, x = 0

3^{1 - 2 x} = 4^{2 x + 5}

3^{4 x} - 3^{2 x} - 6 = 0

(- 3)^{x} = (- 3)^{13}

3^{\frac{x}{4}} = 2

3^{x} = 7^{x}