[Math] way to use a calculator for logarithmic form equations that aren’t base 10 or base e

Question

Is there a way to use a calculator for logarithmic form equations that aren't base 10 or base e?

I just find this really hard to believe and quite unacceptable that the only way to do this is plugging in numbers to find an answer.

Also, it seems this function is probably available because I see a lot of sample problems on tutorials that suggest you do the problems "without a calculator".

I understand the exponential equivalent of logarithmic form but I don't understand why they would say to do these problems without a calculator if calculators don't even do that stuff.

Answer 1

To quote Wikipedia.

$\log_b a = {\log_d a \over \log_d b}$ This identity is useful to evaluate logarithms on calculators. For instance, most calculators have buttons for $\ln$ and for $\log_{10}$, but not for $\log_2$. To find $\log_2 3$, one could calculate $\frac{\log_{10} 3}{\log_{10} 2}$ (or $\frac{\ln 3}{\ln 2}$, which yields the same result).

So to calculate $\log_b a$ Just do $\frac{\ln a}{\ln b}$.

I suspect the reason they do this has to do with a Stack as the internal data structure of the calculator and Prefix / Postfix notation.

When you do $\ln a$ your first type $a$ and then $\ln$ So it primarily takes $1$ operand.