Solve for x 16^(x-1)=8^x

$16^{x - 1} = 8^{x}$

Create equivalent expressions in the equation that all have equal bases.

$2^{4 (x - 1)} = 2^{3 x}$

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$4 (x - 1) = 3 x$

Solve for $x$ .

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Simplify $4 (x - 1)$ .

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Apply the distributive property.

$4 x + 4 \cdot - 1 = 3 x$

Multiply $4$ by $- 1$ .

$4 x - 4 = 3 x$

Move all terms containing $x$ to the left side of the equation.

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Subtract $3 x$ from both sides of the equation.

$4 x - 4 - 3 x = 0$

Subtract $3 x$ from $4 x$ .

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

Solve for x 16^(x-1)=8^x

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