Question

If log 75/16 - 2 log 5/9 + log 32/243 = log p find the value of p

Answer 1

$\log \dfrac{75}{16} - 2 \log \dfrac{5}{9} + \log\dfrac{32}{243} = \log p$

$\log ( \dfrac{75}{16} \div (\dfrac{5}{9} )^2 \times \dfrac{32}{243}) = \log p$

$\log ( \dfrac{75}{16} \div \dfrac{25}{81} \times \dfrac{32}{243}) = \log p$

$\log ( \dfrac{75}{16} \times \dfrac{81}{25} \times \dfrac{32}{243}) = \log p$

$\log (2) = \log p$

$p = 2$

Answer: p = 2