Use the change-of-base property

Question

Use common logarithms or natural logarithms and evaluate to four decimal places.

 

log₁₇76.6

 

 

 

 

 

 

 

( answer is 1.5313 but i need help step by step on how they got this answer)

Answer 1

change of base rule is...

log(b)x=log(a)x/log(a)b

log(17)76.6=log(10)76.6/log(10)17

log(10)76.6=1.88422876963

log(10)17=1.23044892138

1.88422876/1.230448921=1.531334, (you don't have to use so many digits; about 5 in each number should give you the answer)

 

Answer 2

This is a calculator problem.  Many calculators today will have this programmed, so you can just type in the problem as written.  But not too terribly long ago, this was not an option, and you had to use the change of base formula.

 

Using the change of base, you solve this using either common logs or natural logs.  The purpose was that "way back when", you only had access to that data.

 

(log₁₀ 76.6)/(log₁₀17)  ~ Note, log₁₀ is the common logarithm, with the regular log  button on your calculator

OR

(ln 76.6)/(ln17) ~ Note, ln is a log with base e.  Try it both ways, to prove to yourself that you will get the same answer.