Question

Write the expression as a single logarithm: 2logm(8z+1) + logm1/2(z+8)

(A) logm(16z+1) + logm1/2(z+8)
(B) logm(4z+1) + logm1/2(z+8)
(C) logm(8z+1) + logm1/2(z+8)
(D) logm(8z+1) - logm1/2(z+8)

Answer 1

To write the expression as a single logarithm, we can use the properties of logarithms. The property we will use in this case is the addition property: log(m) + log(n) = log(m * n). Using this property, we can rewrite the expression as: 2log(8z+1) + log(1/2)(z+8) = log((8z+1)^2 * (1/2)(z+8)). So the expression can be written as a single logarithm: log((8z+1)^2 * (1/2)(z+8)), which is equivalent to option (A).

Step-by-step explanation:

To write the expression as a single logarithm, we can use the properties of logarithms. The property we will use in this case is the addition property: logb(m) + logb(n) = logb(m * n).

Using this property, we can rewrite the expression as:

2logm(8z+1) + logm(1/2)(z+8) = logm((8z+1)2 * (1/2)(z+8))

So the expression can be written as a single logarithm: logm((8z+1)2 * (1/2)(z+8)), which is equivalent to option (A).