Answer:
The expression is given below as
[tex]\log_{12}7[/tex]
Let the expression above be equal to x
[tex]\log_{12}7=x[/tex]
Concept:
Apply the logarithm change of base formula below
[tex]\begin{gathered} \log_aB=x \\ B=a^x \end{gathered}[/tex]
By applying the concept above we will have
[tex]\begin{gathered} \operatorname{\log}_{12}7=x \\ 12^x=7 \\ take\text{ ln of both sides } \\ ln12^x=ln7 \\ xln12=ln7 \\ divide\text{ both sides by ln 12} \\ \frac{xln12}{ln12}=\frac{ln7}{ln12} \\ x=\frac{ln7}{ln12} \\ x=0.7831 \\ x\approx0.78\left(nearest\text{ hundredth\rparen}\right? \end{gathered}[/tex]
Hence,
The final answer is
[tex]\Rightarrow0.78[/tex]
