Input the base and the number, and quickly calculate the logarithmic value.
A logarithm is a mathematical tool that solves exponential equations. It helps determine how many times a base number must be multiplied by itself to reach another number. For example, given a base \( b \) and a number \( N \), the logarithmic formula is: \( \log_b(N) = x \) This means \( b^x = N \). Logarithms are widely used in fields such as scientific computation and data analysis.
Solution:
\( \log_{10}(100) = x \)
Since \( 10^2 = 100 \), \( x = 2 \).
Result: The logarithm of 100 with base 10 is 2.
Solution:
\( \log_5(625) = x \)
Since \( 5^4 = 625 \), \( x = 4 \).
Result: The logarithm of 625 with base 5 is 4.
Solution:
\( \ln(e^3) = 3 \)
Result: The natural logarithm of \( e^3 \) is 3.