Question

Find the exact solution using common logarithms 2^5x+3= 3^2x+1

Answer 1

$2^{5x + 3} = 3^{2x + 1}$
$log_{2}(2^{5x + 3}) = log_{2}(3^{2x + 1})$
$(5x + 3)log_{2}(2) = (2x + 1)log_{2}(3)$
$5x + 3 = 1.58(2x + 1)$
$5x + 3 = 3.16x + 1.58$
$1.84x + 3 = 1.58$
$1.84x = -1.42$
$x \approx -0.77$