Precalculus Examples

$2 x^{3 x - 5} = 7$

Step 1

Simplify.

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Step 1.1

Divide each term in $2 x^{3 x - 5} = 7$ by $2$ .

$\frac{2 x^{3 x - 5}}{2} = \frac{7}{2}$

Step 1.2

Reduce by cancelling the common factors.

$x^{3 x - 5} = \frac{7}{2}$

Step 2

Convert the exponential equation to a logarithmic equation using the logarithm base $(x)$ of the right side $(\frac{7}{2})$ equals the exponent $(3 x - 5)$ .

$\log_{x} (\frac{7}{2}) = 3 x - 5$