How do you solve #81^ { x ^ { 3} + 2x ^ { 2} } = 27^ { \frac { 5x } { 3} }#?

1 Answer
Vinícius Ferraz
May 27, 2017

#x in {0, - 5/2, 1/2}#

Explanation:

If the constant basis are equal, then the exponents are equal too.

#(3^4)^(x^3 + 2x^2) = 3^(5x)#

#4x^3 + 8x^2 = 5x#

#x = 0 or 4x^2 + 8x - 5 = 0#

In the last case, #Delta = 64 + 4 * 4 * 5 = 144#

#x = (-8 ± 12)/8#

Related questions
Impact of this question
896 views around the world
You can reuse this answer
Creative Commons License