Estimate the common logarithm of $10$ using linear interpolation.

$($a$)$ Interpolate between log $850\mathrm{.}9030900$ and log $1251\mathrm{.}0791812.$

$($b$)$ Interpolate between log $950\mathrm{.}9542425$ and log $1151\mathrm{.}0413927.$

For each of the interpolations, compute the percent relative er$-$

ror based on the true value.