use the properties of logarithms to write the expression as a sum or difference of logarithms or multiples of logarithms.

show your work

Ln 8x

2.

log2y^5

Maybe this helps:

log(AB) = log(A) + log (B)

so for question 1, ln(8x) is ln(x) + ln (8)

log(2y)^5 is 5*log(2y) = 5*(log2 + logy)

Rwsfaherazet

To write the expression Ln 8x as a sum, difference, or multiple of logarithms, we can use the properties of logarithms.

1. Ln 8x:
Using the logarithmic identity Ln(ab) = Ln(a) + Ln(b), we can rewrite Ln 8x as:
Ln 8 + Ln x

Therefore, the expression Ln 8x can be written as the sum of Ln 8 and Ln x.

2. log2y^5:
Using the power rule of logarithms, logb(a^c) = c * logb(a), we can rewrite log2y^5 as:
5 * log2y

Therefore, the expression log2y^5 can be written as the multiple of 5 and log2y.

Sure! Let's go through each expression one by one and use the properties of logarithms to rewrite them.

1. Ln 8x:

The natural logarithm, represented by Ln, has a property called the Product Rule which states that Ln(ab) = Ln(a) + Ln(b) for any positive numbers a and b.

In this case, we have Ln(8x). We can rewrite it using the Product Rule as Ln(8) + Ln(x).

Therefore, the expression Ln 8x can be written as Ln(8) + Ln(x).

2. log2y^5:

The logarithm with base 2, represented by log2, has a property called the Power Rule which states that logb(a^k) = k * logb(a) for any positive numbers a and k.

In this case, we have log2(y^5). We can rewrite it using the Power Rule as 5 * log2(y).

Therefore, the expression log2y^5 can be written as 5 * log2(y).

To summarize:
1. Ln 8x = Ln(8) + Ln(x)
2. log2y^5 = 5 * log2(y)

These are the rewritten forms of the given expressions using the properties of logarithms.