Basic Math Examples

$- 4.53 = \log (z)$

Step 1

Rewrite the equation as $\log (z) = - 4.53$ .

$\log (z) = - 4.53$

Step 2

Rewrite $\log (z) = - 4.53$ 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 $b^{y} = x$ .

$10^{- 4.53} = z$

Step 3

Solve for $z$ .

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Step 3.1

Rewrite the equation as $z = 10^{- 4.53}$ .

$z = 10^{- 4.53}$

Step 3.2

Simplify $10^{- 4.53}$ .

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Step 3.2.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$z = \frac{1}{10^{4.53}}$

Step 3.2.2

Raise $10$ to the power of $4.53$ .

$z = \frac{1}{33884.41561392}$

Step 3.2.3

Divide $1$ by $33884.41561392$ .

$z = 0.00002951$