The logarithmic form of the exponential equation 2³=8 is (D) log₂ 8=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:
The given exponential equation is 2³=8.
To convert the above equation to logarithmic form we have to take logarithm to the base 2 on both sides of the equation.
Taking log₂ on both sides of the equation we get:
log₂(2³)=log₂(8)
Now we know from the properties of logarithms
logₐxⁿ=n logₐx
therefore:
3×log₂(2)=log₂8
Now logₐa=1, so
3×1=log₂8
or, log₂ 8 = 3
Therefore the required logarithmic equation is log₂ 8 = 3.
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