Answer:
D. 0.69
Step-by-step explanation:
Given equation:
[tex]5 \cdot 2^{3x}=21[/tex]
Divide both sides by 5:
[tex]\implies \dfrac{5 \cdot 2^{3x}}{5}=\dfrac{21}{5}[/tex]
[tex]\implies2^{3x}=4.2[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c:[/tex]
[tex]\implies(2^3)^x=4.2[/tex]
[tex]\implies8^x=4.2[/tex]
Take natural logs of both sides:
[tex]\implies \ln 8^x=\ln 4.2[/tex]
[tex]\textsf{Apply the log Power law} \quad \ln x^n=n\ln x :[/tex]
[tex]\implies x \ln 8=\ln 4.2[/tex]
Divide both sides by ln 8:
[tex]\implies \dfrac{x \ln 8}{\ln 8}=\dfrac{\ln 4.2}{\ln 8}[/tex]
[tex]\implies x=\dfrac{\ln 4.2}{\ln 8}[/tex]
[tex]\implies x=0.690129776...[/tex]
[tex]\implies x=0.69 \: \sf (2\:dp)[/tex]
