Final answer:
To condense the expression into a single logarithm, use the logarithmic properties.
Step-by-step explanation:
To condense the expression into a single logarithm, we can use the logarithmic properties. The properties state that loga(b) + loga(c) = loga(b * c) and loga(bc) = c * loga(b).
Using these properties, we can rewrite the expression as log8(w * u1/2 * v1/2). To condense the expression log(8)w + (1)/(2)log(8)u + (1)/(2)log(8)v into a single logarithm, we will apply two properties of logarithms: the power rule logb(an) = n · logb(a), and the product rule logb(xy) = logb(x) + logb(y).
First, we use the power rule to remove the coefficients from the logarithms:
log(8)(w) remains unchanged.
(1)/(2)log(8)u becomes log(8)(u1/2) or log(8)(√u).
(1)/(2)log(8)v becomes log(8)(v1/2) or log(8)(√v).
Combining the above using the product rule, we get:
log(8)(w) + log(8)(√u) + log(8)(√v) = log(8)(w√u√v).
So, the original expression condenses into:
log(8)(w√u√v)