Question

Log(5)(x+4)+log(5)(x+2)=log(5)(7x+10)

Answer 1

 Combine the logarithms first: log5(4x+3)-log5(x-1). Since it's subtract, divide the two. 

log5((4x+3)/(x-1))=2 

Make both sides the exponent of five. 5^log5 cancels out. 

5^(log5(4x+3/x-1))=5^2 

4x+3/x-1=25 

Multiply both sides by (x-1) to get rid of it under 4x+3. 

(x-1)4x+3/x-1=25(x-1) 

4x+3=25x-25 

Now subtract 4x from both sides AND add 25 to both sides. This way you'll have all the x's by itself. 

28=21x 

Divide both sides by 21. 

28/21=x 

x=1.33333333333...