Evaluate the logarithm

log3 729

since 3^6 = 729,

log3 729 = 6

Ah. I see. I understand now. Thank you very much, Steve.

It's pretty much like this:

log3 729= x
3^x= 729
3^x= 3^6
x= 6

exactly. log and power are inverse operations, just like multiply and divide, add and subtract, root and square, etc.

To evaluate the logarithm log3 729, we need to find the exponent to which we must raise the base 3 in order to obtain the number 729.

In other words, we are solving the equation 3^x = 729 for x.

To find the exponent x, we can rewrite 729 as a power of 3:

729 = 3^6

So, we have the equation 3^x = 3^6.

By comparing the exponents, we can deduce that x = 6.

Therefore, log3 729 = 6.