The abbreviation log x is often used when the intended base can be inferred based on the context or discipline, or when the base is indeterminate or immaterial.

Log z = ln (r) + i (θ+2nπ) = ln (√ (x2 + y2)) + i ·arctan (y/x)) Logarithm problems and answers Problem #1 Find x for log 2 (x) + log 2 (x -3) = 2 Solution: Using the product rule: log 2 (x∙ (x -3)) = 2 Changing …

In its simplest form, a logarithm answers the question: How many of one number multiply together to make another number?

This free log calculator solves for the unknown portions of a logarithmic expression using base e, 2, 10, or any other desired base.

Mar 30, 2026 · Expressed mathematically, x is the logarithm of n to the base b if bx = n, in which case one writes x = log b n. For example, 2 3 = 8; therefore, 3 is the logarithm of 8 to base 2, or 3 = log 2 8.

For example the result for 2 x = 5 can be given as a logarithm, x = log 2 (5) . You will learn how to evaluate this logarithmic expression over the following lessons.

The log calculator (logarithm) calculates the value of a logarithm with an arbitrary base.

An exponential equation is converted into a logarithmic equation and vice versa using b x = a ⇔ log b a = x. A common log is a logarithm with base 10, i.e., log 10 = log.

To avoid ambiguity, it is safest to use "log" to refer to base 10 logarithms and "ln" or "natural log" to refer to base e logarithms. In other words, "log (x)" typically indicates log 10 (x) and ln (x) indicates log e (x).

All terms on top of the fraction inside the logarithm are positive and the log (y 5) is subtracted since it has been divided inside the logarithm. We can then use the power law of logarithms to bring down …