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

Question

All bases are 10.

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Answer 1 · 2017-09-14T13:31:04

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

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.#