Question 276285
{{{f(x)=3log(6, (2x-1))}}}
{{{f(5)=3log(6, (2(5)-1))}}}
{{{f(5)=3log(6, (10-1))}}}
{{{f(5)=3log(6, (9))}}}
Now what do we do? How do we find a base 6 logarithm? No calculators I know can do base 6 logarithms. What we need to change the base to one our calculators "know:. Fortunately there is a change of base formula for logarithms: {{{log(a, (p)) = log(b, (p))/log(b, (a))}}}. Using this to change our base 6 log into an expression of base 10 logs we get:
{{{f(5)=3(log((9))/log((6)))}}}
Now we can go to our calculators and find the two base 10 logarithms, divide them and then multiply by 3. (I'll leave that up to you to do.)<br>
P.S. Many calculators also can do base e (ln) logarithms. If we used them instead of base 10 our equation would become:
{{{f(5)=3(ln(9)/ln(6))}}}
Believe it or not, this gives the same answer! (Try it if you don't believe it.)