Question

What is 2logx−logy−2logz

written as a single logarithm?

please help fast

Answer 1

log(x^2/(y z^2)) assuming x, y and z are positive 

Answer 2

The expression written as single logarithm is  log(x²/yz)

Logarithm and indices

According to the laws of logarithm;

• $loga+logb=log(ab)\\loga-logb-log(1/b)$

Given the logarithm expression 2logx−logy−2logz, this can be written as:

logx^2−logy−2logz

= log(x²) - (logy+logz)

= log(x²/yz)

Hence the expression written as single logarithm is  log(x²/yz)

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