Advertisements
Advertisements
Question
Express in terms of log 2 and log 3 :
`"log"75/16 - 2"log"5/9 + "log"32/243`
Solution
`"log"75/16 - 2"log"5/9 + "log"32/243`
= `"log"75/16 - "log"(5/9)^2 + "log"32/243`
= `"log"75/16 - "log"( 5/9 xx 5/9 ) + "log"32/243`
= `"log"75/16 - "log"25/81 + "log"32/243`
= `"log"((75/16)/(25/81)) .....[ log_am - log_an = log_a(m/n)]`
= `"log"(75/16) xx (81/25) + log(32/243)`
= `"log"( 3 xx 25)/16 xx 81/25 + "log"32/243`
= `"log"243/16 + "log"32/243`
= `"log"( 243/16 xx 32/243 )` .....[logam + logan = logamn]
= `"log"32/16`
= log 2
APPEARS IN
RELATED QUESTIONS
Express the following in a form free from logarithm:
a log x - b log y = 2 log 3
Solve for x : log10 (x - 10) = 1
Solve for x : log (x2 - 21) = 2.
Solve for x : log (x + 5) + log (x - 5) = 4 log 2 + 2 log 3
If log102 = a and log103 = b ; express each of the following in terms of 'a' and 'b': log 12
If log102 = a and log103 = b ; express each of the following in terms of 'a' and 'b': log `2 1/4`
Solve for x : ` (log 64)/(log 8)` = log x
State, true or false : log 1 x log 1000 = 0
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.
If log10 8 = 0.90; find the value of : log10 4
