Condense Logarithms Calculator

Your details

Choose the type of expression to condense.
The shared base of both logarithms. Common choices: 2, e (use 2.718), 10.
The number multiplied by the first logarithm. Becomes the exponent via the power rule.
The argument of the first logarithm. Must be positive.
The number multiplied by the second logarithm.
The argument of the second logarithm. Must be positive.
Numeric result
3.54741

Numerical value of the condensed logarithm

Condensed argument576
Condensed expressionlog_6(576)
Original expression3 * log_6(4) + 1 * log_6(9)

Condensed: 3 * log_6(4) + 1 * log_6(9) = log_6(576) = 3.54741

  • The condensed form is log_6(576), which equals approximately 3.54741.
  • The argument inside the condensed logarithm is 576.
  • You can verify the answer by expanding it back: raise the base to the numeric result and check that it equals the condensed argument.

Next stepTo expand a logarithm (reverse this process), use the product, quotient, and power rules in the forward direction, splitting a single log into a sum or difference of logs.

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