Solving this equation logbase2(x+2) + logbase2(x+5) = logbase2(4)

You can use the addition property of logs to turn it into a simple polynomial:

(x + 2)(x + 5) = 4
x^2 + 7x + 10 = 4
x^2 + 7x + 6 = 0

(x + 1)(x + 6) = 0

so x = -1 or x = -6.

Checking these solutions gives (I use lg to mean log base 2):

if x = -1:
lg(1) + lg(4) = lg(4)
which works, since lg(1) = 0

if x = -6:
lg(-4) + lg(-1) = lg(4)
is wonky, so we throw this answer out.


Thus, the solution is x = -1

Hope this helps.

By recalling the property of logarithms which states that:

log(base a) (x) + log(base a) (y) = log(base a) (xy):

log(base 2) (x + 2) + log(base 2) (x + 5) = log(base 2) 4

= log(base 2) [(x + 2)(x + 5] = 2

(x + 2)(x + 5) = 4

x² + 7x + 6 = 0

(x + 6)(x + 1) = 0

x = -1 <-- Answer

x = -6(reject since it leads to a negative inside ln)