How do you convert log base 10 to log base e?

To convert logarithms from base 10 (common logarithm) to base e (natural logarithm), you can use the change of base formula. The change of base formula states that:

log_a(b) = log_c(b) / log_c(a)

In this case, we want to convert log₁₀(x) to log_e(x). We can set ‘c’ as ‘e’ (the base of natural logarithms) and apply the formula:

log₁₀(x) = log_e(x) / log_e(10)

So, if you have a logarithm in base 10, you can find its equivalent in base e by multiplying log_e(x) by log_e(10):

log_e(x) = log₁₀(x) * log_e(10)

To summarize, to convert from log base 10 to log base e, just remember to multiply by the logarithm of 10 in base e.