If the base-10 logarithm of x equals 3, what is the number?

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Multiple Choice

If the base-10 logarithm of x equals 3, what is the number?

Explanation:
Understanding what a base-10 logarithm tells you is the key. The base-10 logarithm of a number x is the exponent you must use on 10 to get x. So if log base 10 of x equals 3, then x equals 10 raised to the 3. That evaluates to 1000, so the number is 1000. The other possibilities would correspond to different exponents: 10 to the 1 is 10, 10 to the 2 is 100, and 10 to the 4 is 10000, which would give logarithms of 1, 2, and 4, not 3.

Understanding what a base-10 logarithm tells you is the key. The base-10 logarithm of a number x is the exponent you must use on 10 to get x. So if log base 10 of x equals 3, then x equals 10 raised to the 3. That evaluates to 1000, so the number is 1000. The other possibilities would correspond to different exponents: 10 to the 1 is 10, 10 to the 2 is 100, and 10 to the 4 is 10000, which would give logarithms of 1, 2, and 4, not 3.

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