Question

18 *2^5t = 261 what is the solution of the equation

Answer 1

Answer:

0.772

Step-by-step explanation:

Original equation:

$18 * 2^{5t}=261$

Divide both sides by 18

$2^{5t} = 14.5$

Rewrite in logarithmic form ($b^x=c \implies log_bc=x$)

$log_214.5 = 5t$

Divide both sides by 5

$\frac{log_214.5}{5}=t$

Rewrite the equation so that base is 10 using change of base formula: $log_ba = \frac{log_na}{log_nb}$

$\frac{(\frac{log14.5}{log2})}{5}=y$

Keep, change, flip

$\frac{log14.5}{log2}*\frac{1}{5} = \frac{log14.5}{5 * log2}$

Use a calculator to approximate log14.5 and log2

$\frac{1.161368}{5 * 0.301029996} = t$

Multiply in denominator

$\frac{1.161368}{1.505149978} = t$

Divide two values

$t\approx 0.771596$

Round to nearest thousandth

$t\approx 0.772$