Question

How do I solve these problems?

ln(x) = 5.6 + ln(7.5)

and

log(x) = 5.6 - log(7.5)

Answer 1

`Domain:\\D:x > 0\\\\\ln x=5.6+\ln(7.5)\ \ \ \ |-\ln(7.5)\\\\\ln x-\ln7.5=5.6\ \ \ |Use\ \log x-\log y=\log(x)/(y)\\\\\ln(x)/(7.5)=5.6\ \ \ \ |use\ \log_ab=c\iff a^c=b\\\\(x)/(7.5)=e^(5.6)\ \ \ \ |\cdot7.5\\\\\boxed{x=7.5e^(5.6)}\in D`

`\log x=5.6-\log7.5\ \ \ \ |+\log7.5\\\\\log x+\log7.5=5.6\ \ \ \ |use\ \log x+\log y=\log (xy)\\\\\log(7.5x)=5.6\ \ \ \ |use\ \log_ab=c\iff a^c=b\\\\7.5x=10^(5.6)\ \ \ \ |:7.5\\\\\boxed{x=(10^(5.6))/(7.5)}\in D`