Question 204023
Using a <i>table</i> of logarithms? I can only guess the problem is meant to force you to learn to "fly on manual".<br>
Let's start by writing the problem as an equation, calling the answer we seek "x":
{{{(0.68)^5 = x}}}
Now we'll find the log of both sides:
{{{log(((0.68)^5)) = log((x))}}}
Next we'll use one of the properties of logarithms which allows us to "remove" an exponent from the argument: {{{log(a^b) = b*log((a))}}}. Using this on our equation to "remove" the 5:
{{{5*log((0.68)) = log((x))}}}
Your table of logarithms probably has columns titled "x" and "log x" or "n" and "log n" or something like that.<ul><li>If the "x" column has a value for .68 then use the value for "log x" across from it.</li><li>If there is no .68 but you have a 6.8 in the "x" column, take the value for "log x" of 6.8 <i>and subtract 1</i>. (This is because .68 = 6.8 x {{{10^(-1)}}}.</li><li>If you have a value for 68 (and not .68 or 6.8) in the "x" column, take the value of "log x" for 68 <i>and subtract 2</i>.</li></ul>
One way or another you should get a number that starts with -0.1<br>
Now we will replace {{{log((0.68))}}} with the -0.1... number:
5*(-0.1....) = log(x)
Now multiply the left side getting something that probably starts with
-0.8...:
-0.8... = log(x)<br>
The last part is to find the number whose log is -0.8.... We do this with the following steps:<ol><li>Since the number is negative, add 1's until it becomes positive. In your case we only need to add 1 once, getting 0.1....</li><li>Go to your table and, <i>under the "log x" column</i>, find the closest number to 0.1....</li><li>Find the number in the "x" column accross from the 0.1... in the "log x" column. This is your answer!</li></ol>