Question

Find c,if 2 raised power a=3 raised power b=6 raised power c?

Answer 1

a=c log(2)6

=>c=a/log(2)6

2^a=6^c

=>2^a=(2^c)(3^c)

=>2^a-c=3^c

now,

3^b=(3^c)(2^c)

=>2^c=3^b-c

=>c=(b-c)log(2)3

=>a/log(2)6=(b-c)log(2)3

=>a=(b-c)log(2)9

and, 2^a=3^b

=>a=b log(2)3

=>b=a/log(2)3

RHS= ab/a+b

=b² log(2)3/b(1+log(2)3)

=b log(2)3-6

=a/log(2)6

=c

=RHS [showed]