Question

Which of the following is equivalent to log408 rounded to three decimal places?

Answer 1

The answer is: $0.564$

The explanation is shown below:

1. To solve this problem you must apply the following proccedure:

2. You have the logarithm expression:

$log40(8)=x$

3. First, you must apply the following property:

$a^{loga(x)} =x$

4. Therefore, you have:

$40^{log40(8)}=40^{x} \\ 8=40^{x}$

5. By applying logarithm on both sides, you have:

$log(8)=log(40^{x} )$

6. By applying the property $log(a)^{b} =blog(a)$:

$log(8)=xlog(40)$

7. Solve for x:

$x=log(8)/log(40)\\ x=0.564$