The expression as a single logarithm is log (2/3).
In mathematics, the inverse function of an exponent is a logarithm. This means that the logarithm of a fixed number, such as a, at base b, is used to represent the exponent to which the fixed number must be raised in order to create the number x.
The general properties of logarithm for a fixed base are:
Now from the above properties of logarithms we can calculate:
log 8-2 log 6+log 3
=log 8 + log 3 - 2log6
We know that logₐx+logₐy=logₐxy and logₐxⁿ=n logₐx
∴log(8×3) -log(6²)
=log 24 - log 36
Again we know that logₐx-logₐy=logₐ(x/y)
=log(24/36)
=log(2/3)
Therefore the given expression written as a single logarithm is log(2/3).
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