Write the expression as a single logarithm whose coeffecient is 1.
Log x + 12 log y
log(xy^12)
To write the expression as a single logarithm with a coefficient of 1, we can apply the logarithmic rule which states that the logarithm of a product is equal to the sum of the logarithms of the individual factors.
Therefore, we can rewrite the given expression:
Log x + 12 log y = log x + log (y^12)
Using the rule, the coefficient 12 moves from being attached to log y to becoming an exponent of y.
Next, we can simplify further by applying the logarithmic rule that states the sum of logarithms can be combined into a single logarithm:
log x + log (y^12) = log (x * y^12)
So, the expression log x + 12 log y can be expressed as the single logarithm log (x * y^12), with a coefficient of 1.