The answer is: [tex] 0.564 [/tex]
The explanation is shown below:
1. To solve this problem you must apply the following proccedure:
2. You have the logarithm expression:
[tex] log40(8)=x [/tex]
3. First, you must apply the following property:
[tex] a^{loga(x)} =x [/tex]
4. Therefore, you have:
[tex] 40^{log40(8)}=40^{x} \\ 8=40^{x} [/tex]
5. By applying logarithm on both sides, you have:
[tex] log(8)=log(40^{x} ) [/tex]
6. By applying the property [tex] log(a)^{b} =blog(a) [/tex]:
[tex] log(8)=xlog(40)
[/tex]
7. Solve for x:
[tex] x=log(8)/log(40)\\ x=0.564 [/tex]
