So this is a simple article of the tips on how to solve the logarithms.
LEVEL : MEDIUM TO HARD
I will solve each question step-by-step, which will come as we progress. Hope you understand them as I will try to make them as simple as I can.
Solve them before watching the solution!
So here the question is clear:
(3x)^(log 3) = (4x)^(log4)
Taking log on both sides,
log3log(3x) = log4log(4x)
log3 . log (3.x) = log4 . log (4.x)
log3 . (log3 + logx) = log4 . (log 4 + logx)
2log3 + (log3 . logx) = 2log4 + (log4.logx)
2(log3 - log4) = log4logx - log3logx
2(log3 - log4) = logx(log4 - log3)
2(log3 - log4) = logx(log(4/3)
x = 2.303(to the base log 10) to the power (2(log3 - log4)/log(4/3))
(Hope you had fun doing this question!)
Let us solve the question step by step:
(a) log(2)y = -3
logy/log2 = -3
log y = -3log2
log y = log(2)^-3
y = 1/8
(b) (log32/log2 + log16/log2)/logx/log2 = logx/log2
Take expand log 2 in the denominator:
(log32 +log16)/log2 / logx/log2 = logx/log2
log 2 cancels out:
log32 + log 16 / log x = logx/log2
log32 +log16 = 2logx/log2
log2 (log32 + log16) = log (x)^2
log2(log(512) = log(x)^2
log2(log(2)^9) = log(x)^2
log2(9log2) = log(x)^2
9(log(2)^2) = 2logx
log (2)^18 = log (x)^2
WHICH IS (512) SQUARED
So x is simply 512!
Thums up if you liked solving them along!
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