Advertisements
Advertisements
Question
Express in terms of log 2 and log 3 :
`"log"75/16 - 2"log"5/9 + "log"32/243`
Advertisements
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
Express log102 + 1 in the form of log10x .
Solve for x : log (x + 5) + log (x - 5) = 4 log 2 + 2 log 3
If log 2 = 0.3010 and log 3 = 0.4771; find the value of:
`2/3` log 8
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`
If log102 = a and log103 = b; express each of the following in terms of 'a' and 'b' : log `3 1/8`
State, true or false :
`log x/log y` = log x - log y
State, true or false :
If `log 25/log 5 = log x`, then x = 2.
If log10 8 = 0.90, find the value of:
log10 4
