how do you change a^2=1.6 into a logarithm?

Question

I understand how to do this with e or ln but not a log

Answer 1

They work the same way as each other ...

You can express exponential equations using logarithms and vice versa:

log_b(expression) = number ... means the same thing as b^number = (expression).

What I tell my students is to remember to keep the bases the same, and the exponent of the base stands alone in the logarithmic expression.

Example:  log₅(25) = 2  means the same thing as 5² = 25

With natural logarithms (where the base is an understood e), you do the same thing...

Example:  ln (4) = 1.3863  means the same thing as  e^1.3863 = 4

Hope this helps you.

Answer 2

Attn: y = a^x is equivalent to log[base a] y = x

So, the log form of a^2 = 1.6 is log[base a] 1.6 = 2.