If a=log23,b=log25andc=log72, then log14063 in terms of a,band c is equal to
[2ac+1][2c+abc+1]
[2ac+1][2a+c+a]
[2ac+1][2c+ab+a]
None of these
Explanation for the correct option:
Step 1. Find the value of log14063 in terms of a,band c:
Given: a=log23,b=log25andc=log72,
log14063 can be written as log2×2×5×73×3×7.
Step 2. Convert log2×2×5×73×3×7 into log2 by changing the base formula.
=log23×3×7log22×2×5×7[∵logab=logablog2a]=log23+log23+log272log22+log25+log27∵log(ab)=loga+logb=2a+log77log722+b+log77log72=2a+1c2+b+1c=2ac+12c+bc+1
Hence, the option(D) is correct.
If a, b, c are pth, qth, and rth terms of a G.P., then (cb)p(ba)r(ac)q is equal to