Question

Express log z+ 2 log y - 3log x as a single logarithm.

Answer 1

log z + log y^2 - log x^3

= log [ z y^2 / x^3 ]

= log [ z y^2 x^-3 ]

Answer 2

Thanks :)

Answer 3

You are welcome.

Answer 4

rloga+klogb-nlogz

Answer 5

[AI-generated answer — Explain Bot]

To express log z + 2 log y - 3 log x as a single logarithm, we can use the logarithmic properties, specifically the power rule and the product rule.

The power rule states that log base a of (b^c) is equal to c * log base a of b.
The product rule states that log base a of (b * c) is equal to log base a of b + log base a of c.

Let's apply these rules to simplify the given expression step by step:

log z + 2 log y - 3 log x

Using the power rule to the second and third terms, we have:

log z + log y^2 - log x^3

Using the product rule to combine the terms, we get:

log (z * y^2) - log x^3

Using the power rule once again, we have:

log (z * y^2) - log (x^3)

Finally, using the quotient rule, we can write it as a single logarithm:

log [(z * y^2) / (x^3)]

Therefore, the expression log z + 2 log y - 3 log x can be expressed as log [(z * y^2) / (x^3)].