quantumliner wrote:

If 3^27^x = 27^3^x , then x is equal to

A.−1

B. 1/2

C.1

D.2

E.-1/2

I scratched my head a lot since I was rusty on these questions and had to view the answer first. I am partly convinced I have found the right path but would welcome any correction

RHS can be rewritten as

(3^3)^3^x

= 3 ^ (3.3^x)

equating powers of matching base from both LHS and RHS.

\(27^x = 3.3^x\)

27^x = 3^(x+1)

LHS can be rewritten.

(3^3)^x= 3^(x+1)

3^3x = 3^(x+1)

equating powers of matching base again

\(3x = x + 1\)

\(2x = 1\)

\(x = 1/2\)

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