Question 382290
{{{2*log(8, (11))}}}
As soon as decimals are mentioned we should recognize that we will probably need our calculators. And our calculators only "know" base 10 and/or base e (aka ln) logarithms. So we need to convert this expression to one involving base 10 or base e logarithms.<br>
Fortunately we have a base conversion formula for logarithms:
{{{log(a, (p)) = log(b, (p))/log(b, (a))}}}
But to use this formula we cannot have a coefficient in front of the logarithm. The simplest way to get rid of the coefficient is to use a property of logarithms, {{{q*log(a, (p)) = log(a, (p^q))}}}, which allows us to move a coefficient into the argument as an exponent. Using this property on your expression we get:
{{{log(8, (11^2))}}}
Since {{{11^2 = 121}}} this becomes:
{{{log(8, (121))}}}
Now we can use the base conversion formula. I will use base e. But you can use base 10 if you want. <i>The final answer will work out the same either way!</i>
{{{ln(121)/ln(8)}}}
{{{4.7957905455967411/2.0794415416798359}}}
2.3062877457581982
Rounded off to two decimal places this is 2.31.