The Purplemath Forums

by **sanman777** on Mon Mar 23, 2009 3:30 pm

need help!

ln(x)-ln(4x-6)=ln(4)

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by **stapel_eliz** on Mon Mar 23, 2009 3:39 pm

sanman777 wrote:need help!

ln(x)-ln(4x-6)=ln(4)

No instructions were included; I'll guess that you're supposed to solve the logarithmic equation.

The first step will be combine the logs on the left-hand side into one term, using log rules.

. . . . . $\ln\left(\frac{x}{4x\, -\, 6}\right)\, =\, \ln(4)$

Then equate the arguments, and solve the resulting rational equation.

. . . . . $\frac{x}{4x\, -\, 6}\, =\, 4$

. . . . . $x\, =\, 4(4x\, -\, 6)$

...and so forth. :wink: