Logarithm Misconceptions Explained

“Hi there! Today, I want to clarify a common misconception in logarithms.

Some students think that xlogb is always the same as log𝑏 to the power of 𝑥. I want you to understand

that this is not true for all values of b. Here’s why: the logarithm function

is only defined for positive real numbers. That means b must be greater than

0, and b must not equal to 1 If b is negative or imaginary, the logarithm logb

is not defined in the real number system. So the so-called equivalence between

𝑥log𝑏 and log𝑏 to the power of 𝑥 breaks down if b is negative. Let me give you an example:

If 𝑏 equals negative 2 and x equals 2 then 𝑥log⁡𝑏 equals two log of negative two. But log of negative two is not defined for real numbers.