Express log z+ 2 log y - 3log x as a single logarithm.
log z + log y^2 - log x^3
= log [ z y^2 / x^3 ]
= log [ z y^2 x^-3 ]
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rloga+klogb-nlogz
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)].