Use logarithms to evaluate the given expression
(7.32^(1/10))*(2470^(30))
The books answer is 7.37 * 10^(101)
I'm not exactly sure how to go about doing this problem.
Let $\displaystyle N = 7.32^{1/10} \cdot 2470^{30}$
Then
$\displaystyle log(N) = log(7.32^{1/10} \cdot 2470^{30})$
(I'm using log to the base 10 but feel free to use any base you desire.)
$\displaystyle log(N) = log(7.32^{1/10}) + log(2470^{30})$
$\displaystyle log(N) = \frac{1}{10}~log(7.32) + 30~log(2470)$
Now grab a calculator:
$\displaystyle log(N) = 101.867$
Now split the integer from the decimal part:
$\displaystyle log(N) = 101 + 0.867$
And raise both sides to the power of 10:
$\displaystyle 10^{log(N)} = 10^{101 + 0.867}$
$\displaystyle N = 10^{0.867} \cdot 10^{101}$
And use your calculator on that first factor:
$\displaystyle N = 7.36817 \times 10^{101}$
Of course you might (as I do) own a calculator that you can multiply the original form out directly.
-Dan