How do you solve 27^(x-3)=1/927x3=19?

1 Answer
Nov 29, 2015

Express as powers of 33 and hence find x = 7/3x=73

Explanation:

If a > 0a>0 then a^(bc) = (a^b)^cabc=(ab)c

So:

3^(3(x-3)) = (3^3)^(x-3) = 27^(x-3) = 1/9 = 3^-233(x3)=(33)x3=27x3=19=32

Since f(x) = 3^xf(x)=3x is a one-one function from RR->(0, oo), the Real solutions of this must have equal exponents:

3(x-3) = -2

Hence:

3x = -2+9 = 7

So x = 7/3