Degrees of Separation to Find Population

$\frac{\ln{\left( x \right)}}{\ln{\left( 10 \right)}} = 2.3$ Multiply both sides by $\ln{\left( 10 \right)}$ : $\ln{\left( x \right)}= 2.3\ln{\left( 10 \right)}$ Take $e$ to the power of both sides: $x = e^{2.3\ln{\left( 10 \right)}}$ Rewrite the exponent: $x = e^{\ln{\left( 10 \right)}\cdot2.3}$ Use Product of Powers property in reverse: $x = {e^{\ln{\left( 10 \right)}}}^{2.3}$ Use the definition of a logarithm: $x = 10^{2.3}$ Rewrite as fractions: $x = 10^{\frac{23}{10}}$ Rewrite the exponent: $x = 10^{\frac{1}{10} \cdot 23}$ Use Product of Powers property in reverse: $x = {10^{\frac{1}{10}}}^{23}$ Use the fact that a fractional exponent is the same as a root: $x = {\sqrt[10]{10}}^{23}$ Use the calculator or any other method you prefer to find this as a decimal approximation $199.526231496\cdots$ . Rounding to the nearest person to avoid saying something gory makes $200$ people.