Question 713101
{{{h= - (100/9)log((p/b))}}}
Substituting in the values given for b and h we get:
{{{2.7 = -(100/9)log((p/31))}}}
And now we solve for p. First we'll isolate the log. Multiplying both sides by -9/100:
{{{(-9/100)*(2.7) = (-9/100)*(-(100/9)log((p/31)))}}}
{{{-.243 = log((p/31))}}}
Next we rewrite the equation in exponential form. In general {{{log(a, (p)) = n}}} is equivalent to {{{p = a^n}}}. Using this pattern (and the fact that the base of "log" is 10) on our equation we get:
{{{10^(-.243) = p/31}}}
Next we multiply both sides by 31:
{{{31*10^(-.243) = p}}}
This is an exact expression for the solution. I'll leave it up to you to use your calculator to find the decimal. (Just be sure to raise 10 to the -.243 power before you multiply by 31.)