Simplify into one logarithm 2 log x + 3 log y

1 answer:

const2013 [10]4 years ago

8 0

If a logarithm has a coefficient, then the coefficient can also be written as the exponent of the input of the logarithm. In other words, if you have the logarithm alog(x), that is equal to log(x^a). So the expression can be rewritten:

log(x^2)+log(y^3)

If tow logarithms of the same bases are added together that is equal to the logarithm of the product of the inputs of the two original logarithms. In other words, given log(x)+log(y), it can also be written as log(xy). So the expression can be combined into one logarithm:

log(x^2 * y^3)

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natka813 [3]

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This is because you're assigning an equation or a number to a letter.

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3 years ago

the intake pipe can fill a certain tank in 6 hours when the outlet pipe is closed, but with the outlet pipe open it takes 9 hour

Leona [35]

The outlet pipe will take 18 hours to empty the tank.

Step-by-step explanation:

Number of hours taken by inlet pipe to fill the tank=6

work done by the inlet pipe in 1 hour=1/6

Number of hours taken by the inlet pipe to fill the tank with the outlet pipe open=9

work done by the inlet pipe in 1 hour with outlet pipe open=1/9

we have to determine the time taken by the outlet pipe to empty the tank

The inlet and outlet pipe does the opposite work.

$\\time\ taken\ by\ the\ outlet\ pipe\ to\ empty\ the\ tank=x\\work\ done\ by\ the\ outlet\ pipe\ in\ 1\ hour=1/x\\(1/6-1/x)9=1\\1/6-1/x=1/9\\1/x=1/6-1/9=3/54\\x=54/3=18$