Question

If l0^x=2 and 5^y = 3
express log 6 in terms of xy​

Answer 1

x + ylog(5)

Explanation:

10^x = 2

log(10^x) = log(2)

x log(10) = log 2

x = log(2)

5^y = 3

log(5^y) = log(3)

ylog(5) = log(3)

log(6) = log(2) + log(3)

log(6) = x + ylog(5)

Answer 2

Log 6 = xlog10 + ylog5

Explanation:

From the question given, we obtained the following information:

l0^x=2

5^y = 3

Log 6 = Log(2 x 3) = log 2 + log 3

Substituting l0^x in place of 2 and 5^y in place of 3, we obtained

log 2 + log 3

Log l0^x + log 5^y

xlog10 + ylog5

Therefore,

Log 6 = xlog10 + ylog5