SOLUTION: I don't know how to use the table of common logs, can you help me compute the following exponent to the nearest ten. {{{10^pi}}} hint {{{pi}}}=3.145926

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Question 764085: I don't know how to use the table of common logs, can you help me compute the following exponent to the nearest ten.
10%5Epi
hint pi=3.145926
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!

log(10p) = p×log(10) = p×(1) = p = 3.14159 = 3 + .14159

The characteristic is 3 and the mantissa is .14159

We look through the body of the log table and we find that .14159
is between the values of .1399 and .1430.  We see that .1399 is the
log of 1.38 and .1430 is the log of 1.39.  We want to know what 
.14159 is the log of.  So we say it is the log of x:

.1399   is the log of 1.38, which means 1.38 = 10.1399
.14159  is the log of x,    which means    x = 10.14159
.1430   is the log of 1.39  which means 1.39 = 10.1430

So we interpolate to find x:

%28matrix%286%2C1%2C%0D%0Athe%2C+difference%2C+between%2C+.14159%2C+and%2C+.1399%29%29matrix%282%2C1%2CIS%2CTO%29%28matrix%286%2C1%2C%0D%0Athe%2C+difference%2C+between%2C+.1430%2C+and%2C+.1399%29%29matrix%281%2C1%2CAS%29%28matrix%286%2C1%2C%0D%0Athe%2C+difference%2C+between%2C+x%2C+and%2C+1.38%29%29matrix%282%2C1%2CIS%2CTO%29%28matrix%286%2C1%2C%0D%0Athe%2C+difference%2C+between%2C+1.39%2C+and%2C+1.38%29%29

%28.14159-.1399%29%2F%28.1430-.1399%29%22%22=%22%22%28x-1.38%29%2F%281.39-1.38%29

.00169%2F.0031%22%22=%22%22%28x-1.38%29%2F.01

.54516 = %28x-1.38%29%2F.01

Multiply both sides by .01

.0054516 = x - 1.38

1.38545 = x, which equals 10.14159

log(10p) = 3 + .14159

Raising 10 to the power of both sides, that is, taking the antilog of
both sides, we have

10p = 103 + .14159

10p = 103×10.14159

10p = 1000×1.38545 = 1385.45

Answer = 1385.45

Edwin