Answer:
0.772
Step-by-step explanation:
Original equation:
[tex]18 * 2^{5t}=261[/tex]
Divide both sides by 18
[tex]2^{5t} = 14.5[/tex]
Rewrite in logarithmic form ([tex]b^x=c \implies log_bc=x[/tex])
[tex]log_214.5 = 5t[/tex]
Divide both sides by 5
[tex]\frac{log_214.5}{5}=t[/tex]
Rewrite the equation so that base is 10 using change of base formula: [tex]log_ba = \frac{log_na}{log_nb}[/tex]
[tex]\frac{(\frac{log14.5}{log2})}{5}=y[/tex]
Keep, change, flip
[tex]\frac{log14.5}{log2}*\frac{1}{5} = \frac{log14.5}{5 * log2}[/tex]
Use a calculator to approximate log14.5 and log2
[tex]\frac{1.161368}{5 * 0.301029996} = t[/tex]
Multiply in denominator
[tex]\frac{1.161368}{1.505149978} = t[/tex]
Divide two values
[tex]t\approx 0.771596[/tex]
Round to nearest thousandth
[tex]t\approx 0.772[/tex]
