If \log_{10}(x) + \log_{10}(5) = 2, what is the value of x? — JAMB UTME

If $\log_{10}(x) + \log_{10}(5) = 2$ , what is the value of $x$ ?

Using the logarithmic product identity

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

, the left side simplifies to

\log_{10}(5x) = 2

. Converting to exponential form gives

5x = 10^2 = 100

, which simplifies directly to

x = 20

Apply the product law of logarithms

\log_{10}(5x) = 2

The sum of logarithms with the same base equals the logarithm of their product:

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

Convert the logarithmic equation to exponential form

5x = 10^2 = 100

By definition of logarithms, if

\log_b(y) = c

, then

y = b^c

Solve for

x

x = \frac{100}{5} = 20

Divide both sides of the linear equation by

5

Logarithmic Product Law and Exponential Conversion

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