Precalculus Examples

$\log (\frac{x}{10^{- 2}}) = 5.4$

Step 1

Simplify $\log (\frac{x}{10^{- 2}})$ .

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Step 1.1

Rewrite $\frac{x}{10^{- 2}}$ as $x {(10^{- 2})}^{- 1}$ .

$\log (x {(10^{- 2})}^{- 1}) = 5.4$

Step 1.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\log (x \cdot 10^{- 2 \cdot - 1}) = 5.4$

Step 1.3

Rewrite $\log (x \cdot 10^{- 2 \cdot - 1})$ as $\log (x) + \log (10^{- 2 \cdot - 1})$ .

$\log (x) + \log (10^{- 2 \cdot - 1}) = 5.4$

Step 1.4

Use logarithm rules to move $- 2 \cdot - 1$ out of the exponent.

$\log (x) - 2 \cdot - 1 \log (10) = 5.4$

Step 1.5

Multiply $- 2$ by $- 1$ .

$\log (x) + 2 \log (10) = 5.4$

Step 1.6

Logarithm base $10$ of $10$ is $1$ .

$\log (x) + 2 \cdot 1 = 5.4$

Step 1.7

Multiply $2$ by $1$ .

$\log (x) + 2 = 5.4$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

No solution

Step 3