Question

solve for x
49^(3x+1)=7^((x^2)+16x+18)

Answer 1

Copy your equation into http://wolframalpha.com

Answer 2

Notice that 49 = 7^2, so the LHS
49^(3x+1) = 7^(6x+2).

Now LHS = RHS if and only if the exponents are equal; i.e,

6x + 2 = x^2 + 16 x + 18
or
x^2 + 10x + 16 = 0.

This is straight-forward to solve.

I recommend NOT using Wolfram, as you'll miss the insight of figuring out the exponents. And you're not going to have Wolfram in your exam either! ;-)

Answer 3

(3x+1)ln(49)=(x^2+16x+18)ln(7)
since ln(49) and ln(7) are constants
get all the variables on one side n solve.

Answer 4

(3x+1)ln(49)=(x^2+16x+18)ln(7)
since ln(7)^2=ln(49)
using this 2ln(7)=ln(49)
2(3x+1)ln(7)=(x^2+16x+18)ln(7)
the ln(7) cancel
leaving
6x+2=x^2+16x+18
0=x^2+10x+16
(x+8)(x+2)=0
x=-8
x=-2