Precalculus Examples

$3 (1 + 10^{7 x}) = 5$

Step 1

Simplify.

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Step 1.1

Divide each term in $3 (1 + 10^{7 x}) = 5$ by $3$ .

$\frac{3 (1 + 10^{7 x})}{3} = \frac{5}{3}$

Step 1.2

Reduce by cancelling the common factors.

$10^{7 x} = \frac{5}{3}$

Step 2

Convert the exponential equation to a logarithmic equation using the logarithm base $(10)$ of the right side $(\frac{5}{3})$ equals the exponent $(7 x)$ .

$\log_{10} (\frac{5}{3}) = 7 x$