Question

solve for x. (ln x)/(ln 3) = lnx-ln3. use a calculatorto evaluate your result, round off to nearest integer

Answer 1

using log properties:
ln(x) - ln(3) = ln(x/3)

Answer 2

then
\[\frac{\ln x}{\ln 3} = \ln(x/3)\]
take e raised to both sides
\[x^{1/\ln 3} = \frac{x}{3}\]

Answer 3

how would we find the numerical answer for this?

Answer 4

divide by x
\[x^{1/\ln 3 - 1} = \frac{1}{3}\]
\[x^{\frac{1-\ln 3}{\ln 3}} = \frac{1}{3}\]
\[x = (\frac{1}{3})^{\frac{\ln 3}{1-\ln 3}}\]