Question

a.) Convert the exponential function below to its corresponding logarithmic function. b.) Write the log form from Part A into the expanded log form.

Answer 1

INFORMATION:

We have the next expression:

$12^3=x^4y^3z^6$

And, we must:

a.) Convert the exponential function below to its corresponding logarithmic function

b.) Write the log form from Part A into the expanded log form

STEP BY STEP EXPLANATION:

a.) To convert it to its corresponding logarithmic function, we must use the next

In our case,

$\begin{gathered} a=3 \\ b=12 \\ n=x^4y^3z^6 \end{gathered}$

Now, replacing in the formula

$log_{12}(x^4y^3z^6)=3$

b.) To write the expanded log form of part A, we must use the properties of log

1. We can separate the multiplications using the first property

$\begin{gathered} log_{12}(x^{4}y^{3}z^{6})=3 \\ log_{12}(x^4)+log_{12}(y^3)+log_{12}(z^6)=3 \end{gathered}$

2. We can delete the exponent of the logarithms using the third property

$4\cdot log_{12}x^{\text{ }}+3\cdot log_{12}y+6\cdot log_{12}z=3$

ANSWER:

a.) The logarithmic function would be:

$log_{12}(x^{4}y^{3}z^{6})=3$

b.) The expanded log form would be:

$4\cdot log_{12}x+3\cdot log_{12}y+6\cdot log_{12}z=3$