Question 74190
I think what you are expressing is x equals the log to the base 11 of 1331.
.
This can be rewritten in exponential form as:
.
{{{11^x = 1331}}}
.
Now you can take the log to the base 10 of both sides to get:
.
{{{log11^x = log 1331}}}
.
By the rules of logs the exponent x comes out as the multiplier of log 11 to give
.
{{{x*log11 = log 1331}}}
.
Now you can use your calculator in log to the base 10 mode to get that log 11 = 1.041392685.
Similarly you can use your calculator in log to the base 10 mode to find that log 1331 =
3.124178055.
.
Substitute these two values into our equation to get:
.
{{{x*(1.041392685) = 3.124178055}}}
.
Now solve for x by dividing both sides by 1.041392685 to get:
.
{{{x = (3.124178055)/(1.041392685) = 3}}}
.
So the answer to this problem is x = 3.
.
Because the values are relatively small, when you got to the exponential form of:
.
{{{11^x = 1331}}}
.
You could have just plugged values in for x until you got to {{{11^3 = 1331}}} but that
is just a "test taking" trick.  The rigorous way to do it is using the procedures above.
. 
Hope this helps you to see your way through this problem.  It has some good practice
with working with logs.