Exponential Form of Logarithm
The exponential form of a logarithm is a way of rewriting a logarithmic equation as an exponential equation.
General Form
If you have a logarithmic equation:
\[ \log_b(x) = y \]It can be rewritten in exponential form as:
\[ b^y = x \]where:
- \( b \) is the base of the logarithm,
- \( x \) is the result,
- \( y \) is the exponent.
Examples
- \[ \log_2(8) = 3 \]\[ 2^3 = 8 \]
- \[ \log_{10}(1000) = 3 \]\[ 10^3 = 1000 \]
Why Use Exponential Form?
- It helps in solving logarithmic equations.
- It makes it easier to understand the relationship between logarithms and exponents.
- It is useful for converting between exponential and logarithmic functions in algebra and calculus.
Latex
b^y = x \iff log_b(x)=y