Linear Algebra Examples

$\ln (175) = 18 \cdot t$

Step 1

Rewrite the equation as $18 \cdot t = \ln (175)$ .

$18 \cdot t = \ln (175)$

Step 2

Divide each term in $18 \cdot t = \ln (175)$ by $18$ and simplify.

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Step 2.1

Divide each term in $18 \cdot t = \ln (175)$ by $18$ .

$\frac{18 \cdot t}{18} = \frac{\ln (175)}{18}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $18$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{18 \cdot t}{18} = \frac{\ln (175)}{18}$

Step 2.2.1.2

Divide $t$ by $1$ .

$t = \frac{\ln (175)}{18}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Rewrite $\frac{\ln (175)}{18}$ as $\frac{1}{18} \ln (175)$ .

$t = \frac{1}{18} \ln (175)$

Step 2.3.2

Simplify $\frac{1}{18} \ln (175)$ by moving $\frac{1}{18}$ inside the logarithm.

$t = \ln (175^{\frac{1}{18}})$

Step 3

The domain is the set of all valid $t$ values.

${t | t = \ln (175^{\frac{1}{18}})}$

Step 4