[MOVED] Logarithm Q: why does log(16)/log(2) = ln(16)/ln(2)?

[lktu]

Why can you use both log and ln when finding a missing exponent. For example log 16/log 2 = 4 and ln 16 / ln 2 = 4.

Why do these two give the same result even though they are different functions and different bases?

Thanks

 

[stapel]

These follow from the change-of-base formula:

. . . . .4 = log₂(16)

. . . . . . .= log₁₀(16) / log₁₀(2)

. . . . . . .= ln(16) / ln(2)

Try proving the change-of-base formula, to explain this to yourself.

. . . . .Change of base: For any bases "b" and "c", the
. . . . .following relation holds:

. . . . . . .log_b(x) = log_c(x) / log_c(b)

If you can prove this, you'll have your proof of why your log relations hold.

Eliz.