Question

how to find the value of log 625/ log √5​

Answer 1

Given:

A logarithmic value log(625)/log(√5).

To Find:

The simplified value of the above form is?

Solution:

The given problem can be solved using the formulae of logarithms.

1. The formulae used to solve the given problem are:

• $log(a^m) = m(loga)$
• $log(\frac{a^b}{c^d}) = \frac{b}{d}(log(\frac{a}{c}) )$
• $\frac{loga}{loga} = 1$

2. Using the above formulae the problem can be simplified,

=> $(\frac{log625}{log\sqrt{5} } ) = (\frac{log5^4}{log(5^{1/2})} )$,

=> $\frac{4log5}{\frac{1}{2}log5 }$,

=> $\frac{4}{\frac{1}{2} }$,

=> $4*2 = 8$.

Therefore, the value of log(625)/log(√5) is 8.

Answer 2

Answer:

The value of ㏒ 625/㏒$\sqrt{5}$ = 8

Step-by-step explanation:      

Given problem ㏒ 625/ ㏒ $\sqrt{5}$  

here  625 can be written as 5⁴

          $\sqrt{5}$   can be written as $5^{ \frac{1}{2} }$  

⇒ ㏒ 625/ ㏒ $\sqrt{5}$  =  ㏒ 5⁴/ ㏒ $5 ^{ \frac{1}{2} }$  

[we know that ㏒ $a^{b}$  = b ㏒ a ]

⇒ ㏒ 5⁴/ ㏒ $5^{ \frac{1}{2} }$  =  4 ㏒ 5/ $\frac{1}{2}$ ㏒ 5

                        = $\frac{4}{ \frac{1}{2} }$   =  4 ×2 = 8

⇒ ㏒ 625/㏒$\sqrt{5}$ = 8