Respuesta :

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]