Write the given expression as a single logarithm. log(70x)+log(10y)-2
log a + log b = log ab
To write the given expression as a single logarithm, we can use the properties of logarithms.
The first property we can use is the addition property of logarithms, which states that log(a) + log(b) = log(ab).
Applying this property to the given expression, we can rewrite it as:
log(70x) + log(10y) - 2 = log(70x) + log(10y) - log(100)
Next, we can use another property of logarithms, which is the subtraction property, stating that log(a) - log(b) = log(a/b).
Using this property, we can simplify the expression further:
log(70x) + log(10y) - log(100) = log((70x * 10y) / 100)
Simplifying the numerator, we have:
log((70x * 10y) / 100) = log((700xy) / 100)
Finally, we can simplify the fraction:
log((700xy) / 100) = log(7xy)
Therefore, the given expression log(70x) + log(10y) - 2 can be written as a single logarithm as log(7xy).