solve log2x = log(x2-35)?

Question

solve log2x = log(x2-35)

NBL im kind a confused about the sin log base 10, how did you came with this?

como, how did you eliminate the log?

Answer 1

First off, the log is an exponent and that is the main method that will solve this problem.

First sin log has base 10, just do
10^(log2x)=10^(logx^2-35), and that will simplify to 2x=x^2-35(This can be proved,but it'll take too long to prove, so just trust me this is right).
So now move everything to one side and then factor:
(x^2)-2x-35=0
(x-7)(x+5)=0
x=7,x=-5

Answer 2

2 x = x ² - 35
x ² - 2 x - 35 = 0
(x - 7) (x + 5) = 0
x = 7 , x = - 5