What is the answer to (8^x+1)/(8^x)=9 ?

The answer to (8^x+1)/(8^x)=9 is x=-1

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(8^x+1)/(8^x)=9

\frac{8 ^{x} + 1}{8 ^{x}} = 9

x = - 1

Solution steps

\frac{8 ^{x} + 1}{8 ^{x}} = 9

Apply exponent rules

(8^{x} + 1) (8^{x})^{- 1} = 9

Rewrite the equation with

8^{x} = u

(u + 1) (u)^{- 1} = 9

Solve

(u + 1) u^{- 1} = 9 : u = \frac{1}{8}

u = \frac{1}{8}

Substitute back

u = 8^{x},

solve for

x

Solve

8^{x} = \frac{1}{8} : x = - 1

x = - 1

Verify Solutions:

x = - 1

True

The solution is

x = - 1

2^{y} = 32

2 7^{2 7^{x + 1}} = 3^{9^{x - 2}}

\frac{3 ^{x}}{9 ^{3 x}} = 81

2 = 1.0 4^{x}

2^{m} = 0.125