Question

logarithm troubles...
how do you solve:
(4^(2x+1))( 5^ (3x-2))=6
please show steps as I will likley have questions for those steps
thank you!!

Answer 1

Take the natural log of both sides and rewrite the left side, originally a product, as a sum of logs\[\ln 4^{2x+1}+\ln 5^{3x-2}=\ln 6\]Pull down exponents and distribute\[2xln4+\ln4+3xln5-2\ln5=\ln6\]Isolate variable containing terms on left \[2xln4+3xln5=\ln6+2\ln5-\ln4\]Facor out x and divide both sides by what is left on left\[x(2\ln4+3\ln5)=\ln6+2\ln5-\ln4\]\[x=\frac{ \ln6+2\ln5-\ln4 }{ 2\ln4+3\ln5 }\]Do you think you can simplify the top and bottom?

Answer 2

now why did you use the natrual log instead of a regular log?

Answer 3

Because the natural log is on most calculators

Answer 4

Sorry, I have to leave.

Answer 5

k thank you