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Question 6

Prove that 9log 4 = 16log 3

Asked by akash kumar | 11th Jul, 2017, 05:13: PM

Expert Answer:

begin mathsize 16px style Consider comma
9 to the power of log 4 end exponent equals straight x
rightwards double arrow open parentheses 3 squared close parentheses to the power of log 4 end exponent equals straight x
rightwards double arrow 3 to the power of 2 log 4 end exponent equals straight x
Taking space log space on space both space sides comma
rightwards double arrow log 3 to the power of 2 log 4 end exponent equals log space straight x
rightwards double arrow 2 log 4 space cross times log 3 equals logx............. left parenthesis straight i right parenthesis
Let comma space 16 to the power of log 3 end exponent equals straight y
rightwards double arrow open parentheses 4 squared close parentheses to the power of log 3 end exponent equals straight y
rightwards double arrow 4 to the power of 2 log 3 end exponent equals straight y
Taking space log space on space both space sides comma
rightwards double arrow log 4 to the power of 2 log 3 end exponent equals logy
rightwards double arrow 2 log 3 cross times space log 4 equals logy........... left parenthesis ii right parenthesis
From space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis
logx equals logy
rightwards double arrow straight x equals straight y
Hence comma space proved space that space
9 to the power of log 4 end exponent equals 16 to the power of log 3 end exponent
end style

Answered by Sneha shidid | 12th Jul, 2017, 09:19: AM