Question

Find the number of digits in 42013 if log10

2

= 0.3010?

Answer 1

Given 4^ 2013
Let us take log 4^2013
= log[(2)²]^2013 [∵ (a^m)^n = a^mn]
= log 2^ 4026
= 4026 log2 [∵ logm^n = nlogm]
= 4026 × 0.301 [∵ log2 = 0.301]
= 1211.826
∴ 4^2013 has 4 digits before decimal

I hope it help u

Answer 2

G.T:

${x}^{2} + {y}^{2} = 6xy$

Adding 2xy on both sides

${x}^{2} + {y}^{2} + 2xy = 6xy + 2xy$

$( x + y)2 = 8xy$

Taking logarithm on both sides

$log \: (x + y)2 = log8xy$

$2.log(x + y) = log8 + log \: x + log \: y$

log xy = log x + log y

$2 \: log \: (x + y) = {log}^{3} + \: log \: x + log \: y$