logarithm of a numbers?

Question

how to express the exponential form to logarithmic form?and give me an example on it

Answer 1

If y=e^x, then x=ln(y), where ln means natural log or log to base e.

If y=2^x then x=log(y), where the log in this case is to base 2. Example: 32=2^5, so 5=log(32) to base 2.

If 10=log(x) where log is to base 2, x=2^10=1024.

If 2^10=10^3 approximately, then 10=3log(10) where log is to base 2, and log(10)=10/3=3.3 approx.

Also 10log2=3 approximately, where log is to base 10, so log2=3/10=0.3 approx.

(log[10](2))(log[2](10))=1 exactly, so log[10](2)=1/(log[2](10)). In fact, log[a](b)=1/(log[b](a)). This is useful when converting logs from one base a to another base b.