Math Worksheet

laws of logarithms

\frac{a}{b}\log c=\log d\cdot x

Enter logarithmic expression in this form \frac{3}{4}\log 27=\log 64\cdot x

Law of Logarithms

laws of logarithms expression

\frac{a}{b}\log c=\log d\cdot x

The expression 2/3 (log 5) = log (4x) means that two-thirds of the logarithm of 5 equals the logarithm of 4x.

Worked example

Let’s say we have the expression 2/3 * log 10 = log 1000.


  • First, we take the logarithm of 1000 to the base 10, which is equal to 3, because 10 raised to the power of 3 is 1000.
  • Next, we divide 2 by 3 which gives us 0.666666… (approximately).
  • So, 0.666666… times the logarithm of 10 is equal to 3 (log 1000).

In simpler terms, when we divide 2 by 3 and multiply it by the logarithm of 10, we get the same result as the logarithm of 1000.


Try Logarithms Base