Question

Use the change of base formula to find log base 6 47. Round to the nearest hundredth.

Answer 1

We need to change the base of the logarithm, one good choice for the new base is "10", because most of the values for logarithms in the base 10 are tabled. To change the base we need to apply the following expression:

`\log _ab=(\log _cb)/(\log _ca)`

Where "c" is the new base, "a" is the old base and "b" is the value we want to calculate. If we change it to the base 10, we have:

`\log _647=(\log _(10)47)/(\log _(10)6)`

We can now solve both logs.

`\log _647=(3.85)/(1.79)=2.149`