Algebra Examples

$4 \cdot 2^{- \frac{t}{5}} = 288$

Step 1

Simplify both sides of the equation.

Tap for more steps...

Step 1.1

Rewrite $4$ as $2^{2}$ .

$2^{2} \cdot 2^{- \frac{t}{5}} = 288$

Step 1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2^{2 - \frac{t}{5}} = 288$

Step 2

Convert the exponential equation to a logarithmic equation using the logarithm base $(2)$ of the right side $(288)$ equals the exponent $(2 - \frac{t}{5})$ .

$\log_{2} (288) = 2 - \frac{t}{5}$