Question

Determine the value of log 3 to the base 81

Answer 1

log 3 base 81=

log81 3=log81 √9=log81 9 1/2

=1/2 log81 9

=log 3 base 81=1/4

Answer 2

The value of log 3 to the base 81 is  $\frac{1}{4}$

Explanation:

Given: $log_{81} 3$

To find: Value of $log_{81} 3$

Formula used: Exponent rule $(x^{a})^{b} = x^{ab}$

Solution.

Take,

$log_{81} 3 = X$

Rewrite the above form as an exponential.

We know that value of the log is the exponent.

From the given value X is the exponent and the 81 is the base.

$log_{81} 3 = X$

So we can write as.

$81^{X} = 3$

Find a common base for both sides, which is 3

$81 = 3^{4}$   so by substitution

$(3^{4})^{X} = 3$

Now use the exponent rule $(x^{a})^{b} = x^{ab}$

$3^{4X} = 3^{1}$

4X = 1

$X = \frac{1}{4}$

Final answer:

The value of log 3 to the base 81 using the exponent form  is  $\frac{1}{4}$

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