What is the answer to 1/8 = 4/(2^{t/7)} ?

The answer to 1/8 = 4/(2^{t/7)} is t=35

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1/8 = 4/(2^{t/7)}

\frac{1}{8} = \frac{4}{2 ^{\frac{t}{7}}}

t = 35

Solution steps

\frac{1}{8} = \frac{4}{2 ^{\frac{t}{7}}}

Apply exponent rules

\frac{1}{8} = 4 \cdot 2^{- \frac{t}{7}}

Multiply both sides by

8

\frac{1}{8} \cdot 8 = 4 \cdot 2^{- \frac{t}{7}} \cdot 8

Simplify

1 = 32 \cdot 2^{- \frac{t}{7}}

Switch sides

32 \cdot 2^{- \frac{t}{7}} = 1

Divide both sides by

32

2^{- \frac{t}{7}} = \frac{1}{32}

Apply exponent rules

- \frac{t}{7} = - 5

Solve

- \frac{t}{7} = - 5 : t = 35

t = 35

Verify Solutions:

t = 35

True

The solution is

t = 35

5^{3 x - 1} = 25

3^{x} = \frac{14}{25}

3^{3 x + 1} = 9^{x + 4}

5^{5 - x} = 2^{5 - x}

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

What is the answer to 1/8 = 4/(2^{t/7)} ?
The answer to 1/8 = 4/(2^{t/7)} is t=35
Solve for t: 1/8 = 4/(2^{t/7)}
The solution is t=35