Solve (1/2)^(4x 1) = (8)^(2x 1)

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Type your math problem... (1/2)^(4x 1) = (8)^(2x 1)

Question

Solve the equation

x = 0

Evaluate

(\frac{1}{2})^{4 x \times 1} = 8^{2 x \times 1}

Multiply the terms

(\frac{1}{2})^{4 x} = 8^{2 x \times 1}

Multiply the terms

(\frac{1}{2})^{4 x} = 8^{2 x}

Rewrite the expression

More Steps

Evaluate

(\frac{1}{2})^{4 x}

Write the number in exponential form with the base of 2

(2^{- 1})^{4 x}

Rewrite the expression

2^{- 4 x}

2^{- 4 x} = 8^{2 x}

Rewrite the expression

More Steps

Evaluate

8^{2 x}

Write the number in exponential form with the base of 2

(2^{3})^{2 x}

Rewrite the expression

2^{6 x}

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

Since the bases are the same,set the exponents equal

- 4 x = 6 x

Add or subtract both sides

- 4 x - 6 x = 0

Subtract the terms

More Steps

Evaluate

- 4 x - 6 x

Collect like terms by calculating the sum or difference of their coefficients

(- 4 - 6) x

Subtract the numbers

- 10 x

- 10 x = 0

Change the signs on both sides of the equation

10 x = 0

Solution

x = 0

Show Solution

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