Question

please help solve for x.. show all steps !!

Answer 1

\[2\log_2 3x - \log_2 5 = \log_2 40 - 3\]\[\log_2 (3x)^2 - \log_2 5 = \log_2 40 - 3\]\[\log_2 9x^2 - \log_2 5 = \log_2 40 - 3\]\[\log_2 \dfrac{9x^2}{5} = \log_2 40 - 3\]\[\log_2 \dfrac{9x^2}{5}-\log_2 40 = - 3\]\[\log_2 \dfrac{\dfrac{9x^2}{5}}{40}= - 3\]\[\log_2 \dfrac{9x^2}{200}= - 3\]Now convert it into exponent equation.
\[2^{-3} = \dfrac{9x^2}{200}\]\[\dfrac{1}{8} = \dfrac{9x^2}{200}\]\[\dfrac{200}{8} = 9x^2\]\[25 = 9x^2\]\[\dfrac{25}{9} = x^2\]\[\boxed{x = \dfrac{5}{3}}\]

Answer 2

Remember, \(\ln a - \ln b = \ln \dfrac{a}{b}\) and \(c \ln a = \ln a^c\)

Answer 3

wow thank you soo much !

Answer 4

You're welcome.