logarithm: figure out log 3.1642 (5) =, which the answer is 1.397

[holiday4ever]

To work out from the calculator for ...
log 3.1642 (5) =
which the answer is 1.397 (tell me if the answer is not correct)

However, how can I work out other way around...
log x (5) = 0.7724

 

[Dr.Peterson]

To work out from the calculator for ...
log 3.1642 (5) =
which the answer is 1.397 (tell me if the answer is not correct)

However, how can I work out other way around...
log x (5) = 0.7724

You need to explain your notation, which is nonstandard. I think, based on your answer, that you meant these: log_3.1642 (5) and log_x (5) = 0.7724, where the subscripts indicate the base of the log. Is that correct?

The key to these is the "change of base formula", log_a(x) = log_b(x)/log_b(a).

Using this, the first question becomes: log_3.1642 (5) = log(5)/log(3.1642) = 1.3972 (using any base for the logs; I used base 10). So, yes, you got that right.

What happens to the second equation using this formula?

 

[Steven G]

However, how can I work out other way around...
log x (5) = 0.7724

You should convert the log equation to an exponential equation....

 

[holiday4ever]

logarithm

You should convert the log equation to an exponential equation....

RE: log_x (5) = 0.7724

Are you able to solve for X?