12) 62x+4 =33x .2x+8
3) 3^{x}.8^{\frac{x}{x+2}} =6
8 Answers
622nd one is not very difficult.. sepereate the powers of 2 and 3 on both sides.. then take log..
ditto with 3...
62x+ log10(2x+1) =log106 +xlog105
or x= log10 (30/2x+1)
Now try this by graph..
10x=30/(2x+1)
Draw the graph..
OOPS i used 2x not 2x
and went mad like hell.. missed a x and what not :P
341x+ \log_{10}(2^x+1) = \log_{10} 6 + x \log_{10} 5 \Rightarrow 10^x(2^x+1) = 6.5^x
\Rightarrow 2^x(2^x+1) = 6
Solving as a quadratic in 2x, and since 2x>0, there's a unique solution 2x=2 or x=1
1Hey Q3 the ans will be
x = 1 , -7/2
Is it???
(taking log 2=0.3 and log 3=0.4)
1Solution for Q1:
x+log10(2x+1) = log106 + xlog105
log1010x+log10(2x+1) = log10(6.5x)
log10(10x(2x+1)) = log10(6.5x)
10x(2x+1) = 6.5x
from hit and trial....
clearly for x=1..... L.H.S = R.H.S...
623^{x}.8^{\frac{x}{x+2}} =6
3x-1=21-3x/(x+2)
3x-1=2(2-2x)/(x+2)
if you take log on both sides from 3x-1=2(2-2x)/(x+2)
you get (x-1) ln 3 = (2-2x)/(x+2) ln 2
Which you can solve and get
x=1 or
(x+2) ln 3 +2ln2 =0
so x+2=ln (4/3)
x= ln 4/3 -2