Solve for x:log(subscribt) 4 (2𝑥+1)= log(subscribe) 4 (𝑥−3)+log 4(subscribt) (𝑥+5)

Question

only the 4 have a subscribt, please help me with a step by step please

Answer 1

Need to use your log rules log a +log b = log AB so the right side of the equation becomes log(4) (x-3)( x+5)and the left side is. log(4 ) (2x+1)

that means that (x-3)(x+5)= 2x+1

x^2 +2x -15 = 2x+1

x^2 -16=0

x=+/-4

now need to check for extraneous solutions . If you use -4 some of your expressions don’t exist since you cannot take the log of a negative number

so the only answer is x=4