What is the answer to 8^{n-1}=sqrt(2) ?

The answer to 8^{n-1}=sqrt(2) is n= 7/6

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8^{n-1}=sqrt(2)

8^{n - 1} = 2

n = \frac{7}{6}

Decimal Notation

n = 1.16666 \dots

Solution steps

8^{n - 1} = 2

Apply exponent rules

3 (n - 1) = \frac{1}{2}

Solve

3 (n - 1) = \frac{1}{2} : n = \frac{7}{6}

n = \frac{7}{6}

(x - 3)^{2 x - 4} = (x - 3)^{x + 3}

(0.1)^{2 x - 4} = 10

3^{30} = 2 7^{y}

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

2^{2 - 3 x} - 8^{x} = - 3