Log2(x+4)+log2(x+1)=1+log2 5

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To solve this logarithmic equation, we will first combine the logarithms on the left side using the product rule of logarithms.

log2((x+4)(x+1)) = 1 + log2(5)

Now, we will simplify the left side by distributing the logarithm.

log2(x^2 + 5x + 4) = 1 + log2(5)

Next, we will convert the equation into exponential form.

2^1 = x^2 + 5x + 4

2 = x^2 + 5x + 4

Now, we will rearrange the equation into standard form.

x^2 + 5x - 2 = 0

Next, we will solve this quadratic equation by factoring or using the quadratic formula.

The factors of -2 that add up to 5 are 6 and -1.

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

Therefore, x = -6 or x = 1.

After analyzing the original equation, we see that x = -6 is an extraneous solution. Thus, the solution to the given equation is x = 1.