Trigonometry Examples

$\log (x y) = 100$

Step 1

Rewrite $\log (x y) = 100$ 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 $b^{y} = x$ .

$10^{100} = x y$

Step 2

Solve for $x$ .

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Step 2.1

Rewrite the equation as $x y = 10^{100}$ .

$x y = 10^{100}$

Step 2.2

Divide each term in $x y = 10^{100}$ by $y$ and simplify.

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Step 2.2.1

Divide each term in $x y = 10^{100}$ by $y$ .

$\frac{x y}{y} = \frac{10^{100}}{y}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $y$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{x y}{y} = \frac{10^{100}}{y}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{10^{100}}{y}$