natural and common logarithms help?

Question

When solving the equations 5^x=20, will you get the same answer when you use common logarithms as when you use natural logarithms? Explain?

Answer 1

Yes you will. In the course of solving, you will use the base change equation, so it really doesnt matter which base you begin with.

x = log 20/log 5
can be any base.

Answer 2

There's only one place where y=5^x and y=20 intersect, so no matter how you solve this equation you must always get the same answer.

Answer 3

for all of these, there's a log button on most scientific and all graphing calculators. just press log or natural log and then the number to get the answer. I don't happen to have a calculator on me but that's how you do them. good luck. d) I know that ln e^17.814 just equals 17.814 because natural logs cancel out logs.

Answer 4

Yes.
ln x=log x * ln 10

using ln
x ln 5=ln 20
x=ln 20 / ln 5

using log you would get
x=log 20 / log 5
x=(ln 20 / ln 10)/(ln 5 / ln 10)

ln 10's cancel so the solutions are identical.
x=1.861