Question

log_2(x+9)+log_2(x+13)=5

Answer 1

Combine the logarithmic expressions using the product rule of logarithms.
log^2((x+9)(x+13))=5

Let both sides of the equation be the exponent of base 2.
2^(log^2((x+9)(x+13)))=2^(5)

Multiply each term in the first group by each term in the second group using the FOIL method. FOIL stands for First Outer Inner Last, and is a method of multiplying two binomials. First, multiply the first two terms in each binomial group. Next, multiply the outer terms in each group, followed by the inner terms. Finally, multiply the last two terms in each group.
(x^(2)+22x+117)=2^(5)

Raising a number to the 5th power is the same as multiplying the number by itself 5 times. In this case, 2 raised to the 5th power is 32.
x^(2)+22x+117=32

To set the left-hand side of the equation equal to 0, move all the expressions to the left-hand side.
x^(2)+22x+85=0

Factor the trinomial
(x+17)(x+5)=0

Set each of the factors of the left-hand side of the equation equal to 0.
x+17=0,x+5=0

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x=-17,-5

Answer 2

Anything not sure?