1.) Write the given expression as a single logarithm.

-2ln(x) +ln (5y)-ln(3z)

2.) Write the given expression as single logarithm.

2log(5x)-5[log(x)-log(y-2)]

3.) Write the given expression as a single logarithm. (Simplify the answer as much as possible.)

ln (e³x⁴)-ln(ey²)+2

4.) Let u = ln(x) and v = ln(y). Write the given expression in terms of u and v following the example below.

ln(x³y)=ln(x³)+ln(y)=3u+v

ln(x⁹y⁸)=

5.)Letu= ln(x) andv= ln(y). Write the given expression in terms ofuandvfollowing the example below.

ln(x³y)=ln(x³)+ln(y)=3u+v

ln (square root of x⁵y/y³)=

6.) The energy intensity i of a sound is related to the loudness of the sound by the function below, where i₀ is the minimum intensity detectable by the human ear and L(i) is measured in decibels. Find the decibel measure of a sound whose intensity is 1,000 times i₀.

L(i)=10 x log (i/i_o)

__________ dB

Please show explanation?