Courses
Courses for Kids
Free study material
Offline Centres
More Last updated date: 02nd Dec 2023
Total views: 384.9k
Views today: 3.84k

# If $\log 625 = k\log 5$, then the value of $k$ is……${\text{A}}{\text{.5}} \\ {\text{B}}{\text{.4}} \\ {\text{C}}{\text{.3}} \\ {\text{D}}{\text{.2}} \$ Verified
Hint – The Problem is given in the term of logarithm so we Use the logarithm formulas i.e $\log {a^b} = b\log a$.
$\;log625 = klog5$
$625 = {5^4},\,\,\,\,\,\,\,\,\,\,...({\text{i}})$
$\log {a^b} = b\log a\,\,\,\,\,\,\,\,\,\,\,\,\,...({\text{ii}})$
From ${\text{(i) & (ii)}}$ the given equation can be
$\log {5^4} = 4\log 5 = k\log 5 \\ 4\log 5 = k\log 5\,\,\,...({\text{iii}}) \\ k = 5\,\,\,\,\,\,({\text{from iii}}) \\$
Hence the value of $k$ is $5$.
Note – To solve these types of problems of logarithms, we must know the basic formula of log and we must also know the way to use it, like here we have first converted the given equation such that identity can be used in it. Here we have used the formula $\log {a^b} = b\log a\,\,$.