Advertisements
Advertisements
प्रश्न
Prove that log 10 125 = 3 (1 - log 10 2)
Advertisements
उत्तर
L.H.S.
= log 10 125
= `"log"_10 (1000/8)`
= log 10 1000 - log 10 8
= log 10 (10)3 - log10(2)3
= 3log 10 10 - 3log 10 2
= 3 x 1 - 3log10 2
= 3(1 - log 10 2)
= R.H.S.
APPEARS IN
संबंधित प्रश्न
Show that : loga m ÷ logab m + 1 + log ab
Given log10x = 2a and log10y = `b/2`. Write 102b + 1 in terms of y.
Evaluate: logb a × logc b × loga c.
Solve : log5( x + 1 ) - 1 = 1 + log5( x - 1 ).
Solve for x, if : logx49 - logx7 + logx `1/343` + 2 = 0
If a2 = log x , b3 = log y and `a^2/2 - b^3/3` = log c , find c in terms of x and y.
Solve the following:
log ( x + 1) + log ( x - 1) = log 11 + 2 log 3
If 2 log x + 1 = log 360, find: log(2 x -2)
Prove that log (1 + 2 + 3) = log 1 + log 2 + log 3. Is it true for any three numbers x, y, z?
Prove that `("log"_"p" x)/("log"_"pq" x)` = 1 + logp q
