If x = log2 and y = log3, express log75 in terms of x and y?

All bases are 10.

1 Answer
Sep 14, 2017

log_(10)75=2-2x+y.

Explanation:

Given that, log_(10)2=x, and, log_(10)3=y.

We will use, in what follows, the familiar Rules of Log. Fun.

We have,

log_(10)75=log_(10)(3xx5^2),

=log_(10)3+log_(10)5^2,

=y+2log_(10)5..........................[because, log_(10)3=y," given],"

=y+2log_(10)(10-:2),

=y+2{log_(10)10-log_(10)2},

=y+2(1-x)............................[because, log_(10)2=x," given]."

rArr log_(10)75=2-2x+y.