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JAMB Mathematics 2011 Paper

Question : 6

Total: 46

If log₃18 + log₃3 - log₃x = 3, Find x.

Solution:

Concept:

Apply the laws of logarithms to combine and simplify the equation.

Explanation:

Given:

\log_3 18 + \log_3 3 - \log_3 x = 3

Rewrite

3

3\log_3 3 = \log_3 3^3 = \log_3 27

Combine the first two logs:

\log_3 18 + \log_3 3 = \log_3(18 \times 3) = \log_3 54

So the equation becomes

\log_3 54 - \log_3 x = \log_3 27

Using the subtraction law:

\log_3\left(\frac{54}{x}\right) = \log_3 27

Since the bases are equal, equate the arguments:

\frac{54}{x} = 27

Solve for

x

x = \frac{54}{27} = 2

Answer:

x = 2

The correct option is B.

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