Pre-Algebra Examples

$20.6 = 8.8 + 5.1 \log (d)$

Step 1

Rewrite the equation as $8.8 + 5.1 \log (d) = 20.6$ .

$8.8 + 5.1 \log (d) = 20.6$

Step 2

Move all terms not containing $\log (d)$ to the right side of the equation.

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Step 2.1

Subtract $8.8$ from both sides of the equation.

$5.1 \log (d) = 20.6 - 8.8$

Step 2.2

Subtract $8.8$ from $20.6$ .

$5.1 \log (d) = 11.8$

Step 3

Divide each term in $5.1 \log (d) = 11.8$ by $5.1$ and simplify.

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Step 3.1

Divide each term in $5.1 \log (d) = 11.8$ by $5.1$ .

$\frac{5.1 \log (d)}{5.1} = \frac{11.8}{5.1}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $5.1$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{5.1 \log (d)}{5.1} = \frac{11.8}{5.1}$

Step 3.2.1.2

Divide $\log (d)$ by $1$ .

$\log (d) = \frac{11.8}{5.1}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $11.8$ by $5.1$ .

$\log (d) = 2.31372549$

Step 4

Rewrite $\log (d) = 2.31372549$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b \neq 1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$10^{2.31372549} = d$

Step 5

Solve for $d$ .

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Step 5.1

Rewrite the equation as $d = 10^{2.31372549}$ .

$d = 10^{2.31372549}$

Step 5.2

Raise $10$ to the power of $2.31372549$ .

$d = 205.93278373$