Finite Math Examples

$5 \ln (8 x) = 20 - 2 \ln (x)$

Step 1

Simplify $5 \ln (8 x)$ .

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Step 1.1

Simplify $5 \ln (8 x)$ by moving $5$ inside the logarithm.

$\ln ({(8 x)}^{5}) = 20 - 2 \ln (x)$

Step 1.2

Apply the product rule to $8 x$ .

$\ln (8^{5} x^{5}) = 20 - 2 \ln (x)$

Step 1.3

Raise $8$ to the power of $5$ .

$\ln (32768 x^{5}) = 20 - 2 \ln (x)$

Step 2

Simplify $- 2 \ln (x)$ by moving $2$ inside the logarithm.

$\ln (32768 x^{5}) = 20 - \ln (x^{2})$

Step 3

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx 3.942549$

Step 4