Question 763120
Given
(1) {{{3^(x+4) = 27^(2x)}}}
Now we know that
(2) {{{27 = 3^3}}} and apply the rule that when we raise a power by an exponent, we multiply the exponents.
For example,
(3) {{{(a^b)^c = a^(b*c)}}}
In our case we have
(4) {{{3^(x+4) = (3^3)^(2*x)}}} or
(5) {{{3^(x+4) = 3^(3^(2*x)) }}} or
(6) {{{3^(x+4) = 3^(6*x)}}}
Now the powers have equal bases on the both sides of (6), so we can equate the exponents and get
(7) x + 4 = 6x or
(8) x = 4/5