Question

!)find the value of log 490 if log 7 is=0.8450
2)given that hcf(306,657) =9 find lcm (306,657)
3)if $x^{2} + y^{2}=6xy$ prove that 2 log(x+y)=Log X+log Y+3 log 2
4)simplify log243 to the base 9

Answer 1

3)X square+Y square=6XY
add 2XY on both the sides 
Xsquare+Ysquare+2XY=6XY+2XY
(X+Y) square=8XY
add log on both sides
2 log (x+y)=log8+logX+logY
(LOGXYZ=LOGX+LOGY+LOGZ)
2 log (x+y)=log2 cube+logx+logy
2 log (x+y)=logx+logy+3log2

4)log243 base 9=x
3 power 5=9 power x
3 power 5=3 power 2x
bases are equal ,equate the powers
5=2x
5/2=x

Answer 2

1) log 490 =Log ( 49*10) =Log 49 + log 10 =Log 7^2 + log 10 =2 log 7 + 1 =2*0.8450 + 1 =1.69 + 1 =2.69 2) HCF (306,657) = 9 LCM (306,657) = LCM (2*3*3*17, 3*3*73) = 2*3*3*17*73 = 22338