Mathematics: Write the expression below so that only a single logarithm or exponential function appears.. (1/2)ln(z) − ln(5 + x) − 4 ln(y)

thank you for staying home Step-by-step explanation:...

Write the expression below so that only a single

Ответ:

rose3358

07.01.2022

Mathematics

The answer is:

$ln(\frac{z^\frac{1}{2}}{(5+x)*(y^4)} )$

Step-by-step explanation:

In order to determine the answer, we have to know about the properties of the logarithmic.

For this case, we need three properties. It is very important that these properties assume that the base of the logarithmic is the same. In this case we have the base "e" (euler number).

We can separate the power inside of the logarithmic: ln(a^b)=b*ln(a)

. We can join the sum of logarithmics into a product: ln(a)+ln(b)=ln(a*b)

We can join the subtraction of logarithmics into a division: $ln(a)-ln(b)=ln(\frac{a}{b})$

Applying these properties:

$\frac{1}{2}ln(z)=ln(z^\frac{1}{2})\\\\4ln(y)=ln(y^4)\\\\ln(z^\frac{1}{2})-ln(5+x)-ln(y^4)\\ln(z^\frac{1}{2})-(ln(5+x)+ln(y^4))\\ln(z^\frac{1}{2})-(ln((5+x)*(y^4)))\\ln(\frac{z^\frac{1}{2}}{(5+x)*(y^4)} )$

Finally, the expression is:

$ln(\frac{z^\frac{1}{2}}{(5+x)*(y^4)} )$

0,0(0 оценок)

Write the expression below so that only a single logarithm or exponential function appears.. (1/2)ln(z) − ln(5 + x) − 4 ln(y)

Ответ:

Ответ:

Ask your question to the AI advisor

More tips

Answers on questions: Mathematics

Ask an AI advisor a question