If \log_2 (x + 3) + \log_2 4 = 5, what is the value of x? — JAMB UTME

If $\log_2 (x + 3) + \log_2 4 = 5$ , what is the value of $x$ ?

The value of

x

5

Using the logarithmic addition property

\log_b (M) + \log_b (N) = \log_b (M \cdot N)

, the equation

\log_2(x+3) + \log_2 4 = 5

becomes

\log_2[4(x+3)] = 5

. Converting to index form gives

4(x+3) = 2^5 = 32

. Dividing by

4

yields

x + 3 = 8

, so

x = 5

Apply the product rule of logarithms:

\log_b A + \log_b B = \log_b (A \cdot B)

\log_2 [4(x + 3)] = 5

Logarithms with the same base that are added together can be combined by multiplying their arguments.

Convert the logarithmic equation into its equivalent exponential form

4(x + 3) = 2^5 = 32

\log_b Y = c

, then

Y = b^c

Divide both sides by 4 and solve for

x

x + 3 = 8 \implies x = 5

Linear algebraic simplification.

Product Law of Logarithms and Log-to-Exponential Conversion

Question