Trigonometry Examples

$9.76 = 0.67 \log (0.37 x)$

Step 1

Rewrite the equation as $0.67 \log (0.37 x) = 9.76$ .

$0.67 \log (0.37 x) = 9.76$

Step 2

Divide each term in $0.67 \log (0.37 x) = 9.76$ by $0.67$ and simplify.

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Step 2.1

Divide each term in $0.67 \log (0.37 x) = 9.76$ by $0.67$ .

$\frac{0.67 \log (0.37 x)}{0.67} = \frac{9.76}{0.67}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $0.67$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{0.67 \log (0.37 x)}{0.67} = \frac{9.76}{0.67}$

Step 2.2.1.2

Divide $\log (0.37 x)$ by $1$ .

$\log (0.37 x) = \frac{9.76}{0.67}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $9.76$ by $0.67$ .

$\log (0.37 x) = 14.56716417$

Step 3

Rewrite $\log (0.37 x) = 14.56716417$ 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 $b^{y} = x$ .

$10^{14.56716417} = 0.37 x$

Step 4

Solve for $x$ .

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Step 4.1

Rewrite the equation as $0.37 x = 10^{14.56716417}$ .

$0.37 x = 10^{14.56716417}$

Step 4.2

Divide each term in $0.37 x = 10^{14.56716417}$ by $0.37$ and simplify.

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Step 4.2.1

Divide each term in $0.37 x = 10^{14.56716417}$ by $0.37$ .

$\frac{0.37 x}{0.37} = \frac{10^{14.56716417}}{0.37}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $0.37$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{0.37 x}{0.37} = \frac{10^{14.56716417}}{0.37}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{10^{14.56716417}}{0.37}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Raise $10$ to the power of $14.56716417$ .

$x = \frac{369117111886792}{0.37}$

Step 4.2.3.2

Divide $369117111886792$ by $0.37$ .

$x = 997613815910248.\overline{648}$