Value of 2log420006 + 3log520006 is a) 413 512 - Maths - Mathematical Reasoning

Question

Value of 2 log 4 2000 6   +   3 log 5 2000 6 is

a) 4 1 3     5 1 2 b) 1 6 c) 4 3 d) None of these

Lovina Kansal · Accepted Answer

Dear student
We have,2log420006+3log520006Let 20006=xSo, 2log4x+3log5x=2log10xlog104+3log10xlog105    As logbx=log10xlog10b=2log104log10x+3log105log10x=2×log104log10x+3×log105log10x=2×log104+3×log105log10x=log1042+log1053log10x=log1016+log10125log10x=log1016×125log10x=log102000log10x=log102000log1020006=log1020006log102000=16
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Value of 2 log 4 2000 6 + 3 log 5 2000 6 is a) 4 1 3 . 5 1 2 b) 1 6 c) 4 3 d) None of these

Value of $[\frac{2}{\log_{4} {(2000)}^{6}} + \frac{3}{\log_{5} {(2000)}^{6}}]$ is

a) $4^{\frac{1}{3}} . 5^{\frac{1}{2}}$ b) $\frac{1}{6}$ c) $\sqrt[3]{4}$ d) None of these