# Math Help - Use Logarithms to evaluate the expression

1. ## Use Logarithms to evaluate the expression

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.

2. Originally Posted by OzzMan
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 $N = 7.32^{1/10} \cdot 2470^{30}$

Then
$log(N) = log(7.32^{1/10} \cdot 2470^{30})$
(I'm using log to the base 10 but feel free to use any base you desire.)

$log(N) = log(7.32^{1/10}) + log(2470^{30})$

$log(N) = \frac{1}{10}~log(7.32) + 30~log(2470)$

Now grab a calculator:
$log(N) = 101.867$

Now split the integer from the decimal part:
$log(N) = 101 + 0.867$

And raise both sides to the power of 10:
$10^{log(N)} = 10^{101 + 0.867}$

$N = 10^{0.867} \cdot 10^{101}$

And use your calculator on that first factor:
$N = 7.36817 \times 10^{101}$

Of course you might (as I do) own a calculator that you can multiply the original form out directly.

-Dan

3. Thanks. Makes sense now. My calculator gets overflow when i multiply it directly out though.