Real Number Quiz 10

A sweet seller has 420 Kaju burfies and 130 Badam burfies. She wants to stock them in such a way that each stock has the same number and they take up the least area of the tray. What is the number of burfies that can be placed in each stock for this purpose ?

If $log_{10}3$ = 0.4771, then the value of log 15 + log 2 = …………

Find the value of $log_\frac{4}{3} \, \frac{256}{81}$

$(X^a . X^b )^{a-b} (X^b . X^c )^{b-c} (X^c . X^a )^{c-a}$ = ……………

If $x^{1-log _5^x}\,=$ 0.04 then x = ……………

If $log_{10}343$ = 2.5353, then the least positive integer ‘n’ such that $7^n$ > $10^5$  is 

If $x^2+y^2=6xy$  then $2\,log(x+y)-log(xy)$ = ……………

$\frac{4}{9^{\frac{1}{3}}-{3}^{\frac{1}{3}}+1} =A . 3^{\frac{1}{3}}$ + B then

$x=3+2\sqrt2$ then $x^4+\frac{1}{x^4}$ = ………...

$x=\frac{\sqrt2+1}{\sqrt2-1} , y=\frac{\sqrt2-1}{\sqrt2+1}$ then $x^2-xy+y^2$  = …………