Precalculus Examples

$f (4.9) = \frac{(4.9) - 5}{{(4.9)}^{2} - 25}$

Step 1

Simplify.

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Step 1.1

Multiply each term in $f (4.9) = \frac{(4.9) - 5}{{(4.9)}^{2} - 25}$ by $(4.9) - 5$ .

$f (4.9) ((4.9) - 5) = \frac{4.9 - 5}{{(4.9)}^{2} - 25} (4.9 - 5)$

Step 1.2

Move $4.9$ to the left of $f$ .

$4.9 f ((4.9) - 5)$

Step 1.3

Subtract $5$ from $4.9$ .

$4.9 f \cdot - 0.1$

Step 1.4

Multiply $- 0.1$ by $4.9$ .

$- 0.49 f$

Step 1.5

Reduce by cancelling the common factors.

$- 0.49 f = {(4.9)}^{2}$

Step 2

Convert the exponential equation to a logarithmic equation using the logarithm base $(4.9)$ of the left side $(- 0.49 f)$ equals the exponent $(2)$ .

$\log_{4.9} (- 0.49 f) = 2$