MATHEMATICS

JAMB 2011 - Question 7

Mathematics 2011 JAMB Past Questions - Question 7: If log318 + log33 - log3x = 3, Find x.

If log318 + log33 - log3x = 3, Find x.
A:
B:
C:
D:
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Correct Answer

B

Explanation

If log₃ 18 + log₃ 3 – log₃ x = log₃27log₃ (18 x 3/x) = log₃2718 x 3 = 27 27x = 54 = 54/27 = 2To solve the equation log₃ 18 + log₃ 3 - log₃ x = 3, we can use the properties of logarithms to simplify it.First, we can combine the logarithms using the product and quotient rules:log₃ 18 + log₃ 3 - log₃ x = log₃ (18 * 3 / x)Next, we can simplify the right side of the equation:log₃ (18 * 3 / x) = log₃ (54 / x)Now, we can rewrite the equation as an exponential equation:3^3 = 54 / xSimplifying further:27 = 54 / xTo isolate x, we can multiply both sides of the equation by x:27x = 54Finally, we can solve for x by dividing both sides of the equation by 27:x = 54 / 27Simplifying:x = 2Therefore, the value of x that satisfies the equation is 2.