Question

log5 0.2 is equal to

Answer 1

Answer:

-1

Step-by-step explanation:

Concept:

1.Quotient rule of logarithm:

$log_a(\frac{M}{N})=log_{a}M-log_{a}N$

2.logarithm of 1 to any base is 0

That is, $log_{a}1=0$

$log_{5}(0.2)\\\\=log_{5}(\frac{1}{5})\\\\=log_{5}1-log_{5}5$

= 0-1

=- 1

Answer 2

Answer:

$\log_5 (0.2)=-1$  

Step-by-step explanation:

Given : Expression  $\log_5 (0.2)$

To find : The value of the expression?

Solution :

Re-write the expression using change of base formula,

$\log_a x=\frac{\log_b (x)}{\log_b(a)}$

Here, a=5 and x=0.2 let b=10

Substitute in the formula,

$\log_5 (0.2)=\frac{\log_{10} (0.2)}{\log_{10}(5)}$

$\log_5 (0.2)=\frac{\log_{10} (\frac{1}{5})}{\log_{10}(5)}$

Apply logarithmic identity, $\log(\frac{a}{b})=\log a-\log b$

$\log_5 (0.2)=\frac{\log 1-\log 5}{\log 5}$

$\log_5 (0.2)=\frac{\log 1}{\log 5}-\frac{\log 5}{\log 5}$

$\log_5 (0.2)=0-1$

$\log_5 (0.2)=-1$