Answer:
Part 1) [tex]log_5 (42)=2.3223[/tex]
Part 2) [tex]log_5 (42)=\frac{log_8(42)}{log_8(5)}[/tex]
Step-by-step explanation:
we know that
The [tex]log_a (x)[/tex] can be converted to the base b by the formula
[tex]log_a (x)=\frac{log_b(x)}{log_b(a)}[/tex]
Part 1) Calculate [tex]log_5 (42)[/tex]
Convert to base 10
[tex]log_5 (42)=\frac{log_1_0(42)}{log_1_0(5)}=\frac{log(42)}{log(5)}=2.3223[/tex]
Part 2) Rewrite as logarithm to the base 8
we know that
The [tex]log_a (x)[/tex] can be converted to the base b by the formula
[tex]log_a (x)=\frac{log_b(x)}{log_b(a)}[/tex]
In this problem we have
[tex]log_5 (42)[/tex]
Applying the formula
Changing the base of a logarithm
[tex]log_5 (42)=\frac{log_8(42)}{log_8(5)}[/tex]