How do you solve #16^ { 2x - 3} = 4^ { x ^ { 2} + 17x + 30}#?

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Answer 1 · 2017-11-13T12:46:09

see below.

If the bases are equal, then the exponents are equal. So we try and represent both sides with the same base.

#16=4^2#

#:.#

#((4)^2)^(2x-3)=(4)^(2(2x-3))= 4^(4x-6)#

So:

#4^(4x-6)=4^(x^2+17x+30)#

And:

#4x-6=x^2+17x+30#

#-> x^2+13x+36=0#

Solve for #x#

Factor:

#(x+9)(x+4)=0=>x=-9 and x=-4#