Advertisements
Advertisements
Question
If log102 = a and log103 = b ; express each of the following in terms of 'a' and 'b': log 12
Solution
Given that log102 = a and log103 = b
log 12
= log 2 x 2 x 3
= log 2 x 2 + log 3 ...[ logamn = logam + logan ]
= log 22 + log 3
= 2log 2 + log 3 ...[ nlogam = logamn ]
= 2a + b ...[ ∵ log102 = a and log103 = b ]
APPEARS IN
RELATED QUESTIONS
Evaluate the following without using tables :
log108 + log1025 + 2 log103 - log1018
Evaluate the following without using tables :
log 4 + `1/3` log 125 - `1/5`log 32
Prove that : `2"log" 15/18 - "log"25/162 + "log"4/9 = log 2 `
Find x, if : x - log 48 + 3 log 2 = `1/3`log 125 - log 3.
Solve for x : `(log 81)/(log27 )` = x
If log 2 = 0.3010 and log 3 = 0.4771; find the value of : log 25
If log102 = a and log103 = b ; express each of the following in terms of 'a' and 'b' : log 5.4
If log102 = a and log103 = b; express each of the following in terms of 'a' and 'b' : log 60
State, true or false :
`log x/log y` = log x - log y
Given that log x = m + n and log y = m - n, express the value of log ` ( 10x ) / ( y ^ 2 )` in terms of m and n.
