Basic Math Examples

$\log (y) = 0.98 \cdot \log (k) + 1.09$

Step 1

Simplify the right side.

$\log (y) = 0.98 \log (k) + 1.09$

Step 2

Move all the terms containing a logarithm to the left side of the equation.

$\log (y) - 0.98 \log (k) = 1.09$

Step 3

Simplify the left side.

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Step 3.1

Simplify $\log (y) - 0.98 \log (k)$ .

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Step 3.1.1

Simplify $- 0.98 \log (k)$ by moving $0.98$ inside the logarithm.

$\log (y) - \log (k^{0.98}) = 1.09$

Step 3.1.2

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log (\frac{y}{k^{0.98}}) = 1.09$

Step 4

Rewrite $\log (\frac{y}{k^{0.98}}) = 1.09$ 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 $b^{y} = x$ .

$10^{1.09} = \frac{y}{k^{0.98}}$

Step 5

Solve for $y$ .

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Step 5.1

Rewrite the equation as $\frac{y}{k^{0.98}} = 10^{1.09}$ .

$\frac{y}{k^{0.98}} = 10^{1.09}$

Step 5.2

Multiply both sides by $k^{0.98}$ .

$\frac{y}{k^{0.98}} k^{0.98} = 10^{1.09} k^{0.98}$

Step 5.3

Simplify.

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Step 5.3.1

Simplify the left side.

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Step 5.3.1.1

Cancel the common factor of $k^{0.98}$ .

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Step 5.3.1.1.1

Cancel the common factor.

$\frac{y}{k^{0.98}} k^{0.98} = 10^{1.09} k^{0.98}$

Step 5.3.1.1.2

Rewrite the expression.

$y = 10^{1.09} k^{0.98}$

Step 5.3.2

Simplify the right side.

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Step 5.3.2.1

Raise $10$ to the power of $1.09$ .

$y = 12.3026877 k^{0.98}$