To solve the given problem, we first express
a,c, and
e in terms of
p using the provided logarithmic relationships:
loga=p implies
a=10plogc=2p implies
c=102ploge=3p implies
e=103pNext, we need to find
( ace ). First, compute ace:
ace=10p⋅102p⋅103pUsing the laws of exponents, we combine the terms:
ace =10p+2p+3p=106pNow, raise ace to the power of
:
( ace )=(106p)Using the power rule of exponents,
(am)n=amn, we get:
(106p)=106p⋅=106The expression
106 represents
106, which corresponds to a specific combination of letters as presented in the given options.
Among the provided options, Option A
(bd2f3) is the correct match because it correctly utilizes the exponents 1,2 , and 3 respectively, matching the total exponent of 6 derived above.