Question

Exponential and logarithmic functions are inverses of each other how?​

Answer 1

Exponential and logarithmic functions are inverses of each other, meaning each can 'undo' the effect of the other. The natural logarithm of the exponential function returns the original variable, and raising the base e to the power of a natural logarithm does the same.

Step-by-step explanation:

Exponential and logarithmic functions are mathematical inverses of each other, which means that they 'undo' one another. For instance, taking the natural logarithm (ln) of an exponential function (ex) will return the original variable, so ln(ex) = x. Conversely, raising the natural number e to the power of a logarithmic function returns the input of the logarithm, so eln(x) = x.

In the case of common logarithms (log), similar relationships hold true. If you raise 10 to the power of the logarithm of a number, you get the original number back: 10log(x) = x. This relationship applies to any logarithmic base and is foundational to understanding the way logarithms simplify multiplicative and division operations into additive and subtractive ones, respectively. For instance, the logarithm of a product is the sum of the logarithms: log(xy) = log(x) + log(y), and the logarithm of a quotient is the difference: log(x/y) = log(x) - log(y).

Answer 2

The template for a logarithm is:

a^c = b

log a b = c

This may not make sense on it's own so I will include an example - see the attachment:

2^3 = 8

log 2 8 = 3

2 cubed (to the power of 3) = 8

2 * 2 * 2 = 8

2, multiplied by itself, goes into 8 3 times.