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Class 10 > Learn Mathematics > Find constant A such that log base 3 x = A log base...
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Find constant A such that log base 3 x=A log base 5 x for all x > 0?

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log 3 to the base 5.
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We know that, log 'x' to base 'y' = log 'x' to base ' z ' * log'z' to base' y' ............. (1) and log 'p' to base 'q' = 1/ log 'q' to base 'x' ............(2) In the present context, It is given that log 'x' to base '3' = A log 'x'to base '5' by using formula (2) above, we can rewrite this equation...
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We know that, log 'x' to base 'y' = log 'x' to base ' z ' * log'z' to base' y' ............. (1) and log 'p' to base 'q' = 1/ log 'q' to base 'x' ............(2) In the present context, It is given that log 'x' to base '3' = A log 'x'to base '5' by using formula (2) above, we can rewrite this equation as:- log 'x' to base '3' = A * 1/ log '5' to base 'x' ==> log '5' to base 'x' * log 'x' to base '3' = A==> log '5' to base '3' = A ( [By using the Formula (1) above, (log'5' to base 'x' * log 'x' to base '3') becomes (" log '5' to base '3'). Therefore, A = log 5 to base 3. read less
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