Question

7 log(3x) + 3 log (5x)= 15

Answer 1

$log(3x)^{7} + log(5x)^{3} = 15$

$log((3x)^{7} * (5x)^{3} ) = 15$

$log(3^{7}x^{7} * 5^{3}x^{3} ) = 15$

$log((3^{7}*5^{3})x^{7+3}) = 15$

$log(15^{10}x^{10} ) = 15$

$15^{10}x^{10} = 10^{15}$

$\sqrt[10]{15^{10}x^{10}} = \sqrt[10]{10^{15}}$

15x = $\sqrt[10]{10^{10}*10^{5}}$

15x = $10\sqrt[10]{10^{5}}$

x = $\frac{10\sqrt[10]{10^{5}}}{15}$ = $\frac{2\sqrt[10]{10^{5}}}{3}$