Calculus Examples

$4.9 = 4.74 + \log (\frac{x}{0.1})$

Step 1

Rewrite the equation as $4.74 + \log (\frac{x}{0.1}) = 4.9$ .

$4.74 + \log (\frac{x}{0.1}) = 4.9$

Step 2

Move all terms not containing $\log (\frac{x}{0.1})$ to the right side of the equation.

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Step 2.1

Subtract $4.74$ from both sides of the equation.

$\log (\frac{x}{0.1}) = 4.9 - 4.74$

Step 2.2

Subtract $4.74$ from $4.9$ .

$\log (\frac{x}{0.1}) = 0.16$

Step 3

Rewrite $\log (\frac{x}{0.1}) = 0.16$ 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 $b^{y} = x$ .

$10^{0.16} = \frac{x}{0.1}$

Step 4

Solve for $x$ .

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Step 4.1

Rewrite the equation as $\frac{x}{0.1} = 10^{0.16}$ .

$\frac{x}{0.1} = 10^{0.16}$

Step 4.2

Multiply both sides of the equation by $0.1$ .

$0.1 \frac{x}{0.1} = 0.1 \cdot 10^{0.16}$

Step 4.3

Simplify both sides of the equation.

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Step 4.3.1

Simplify the left side.

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Step 4.3.1.1

Cancel the common factor of $0.1$ .

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Step 4.3.1.1.1

Cancel the common factor.

$0.1 \frac{x}{0.1} = 0.1 \cdot 10^{0.16}$

Step 4.3.1.1.2

Rewrite the expression.

$x = 0.1 \cdot 10^{0.16}$

Step 4.3.2

Simplify the right side.

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Step 4.3.2.1

Simplify $0.1 \cdot 10^{0.16}$ .

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Step 4.3.2.1.1

Raise $10$ to the power of $0.16$ .

$x = 0.1 \cdot 1.44543977$

Step 4.3.2.1.2

Multiply $0.1$ by $1.44543977$ .

$x = 0.14454397$