Solve \log _2\left(4^{3x-1}\right)=25^{\log _5\left(2

Evaluate

lo g_{2} (4^{3 x - 1}) = 2 5^{l o g_{5} (2)}

Evaluate the logarithm

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2 (3 x - 1) = 2 5^{l o g_{5} (2)}

Transform the expression

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

Divide both sides

\frac{2 ( 3 x - 1 )}{2} = \frac{2 ^{2}}{2}

Divide the numbers

3 x - 1 = \frac{2 ^{2}}{2}

Divide the numbers

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3 x - 1 = 2

Move the constant to the right side

3 x = 2 + 1

Add the numbers

3 x = 3

Divide both sides

\frac{3 x}{3} = \frac{3}{3}

Divide the numbers

x = \frac{3}{3}

Solution

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x = 1

Solve the equation