SOLUTION: using the law of logarithms how would you rewrite the following equation as one logarithm? {{{ln5+ln5^2+ln5^3-ln5^6}}} I keep getting 0 but the answers in the back of the boo

Question 231883: using the law of logarithms how would you rewrite the following equation as one logarithm?

I keep getting 0 but the answers in the back of the book is is this equivilant to 0? How did they get this answer?
(those are natural log functions, I thought it would much be harder to understand if written using log form)

Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
Here's a couple of ways to simplify this expression:

Use the following property of logarithms, , to "move" the exponent in the argument out in front, which changes

into

Adding like terms:

which simplifies to:
Use the following properties of logarithms:
to "combine" the logarithms. This will change

into

Using our rules for exponents to multiply the numerator:

And since any non-zero number divided by itself is 1:

This expression represents the exponent for e which results in 1. Since any non-zero number, including e, to the zero power is 1, = ..., we get

RELATED QUESTIONS
Rewrite the expression ln5 + 5lnx + 2ln(x^2+6) as a single logarithm lnA. Then the... (answered by reviewermath)

Write the following expressions as the logarithm of a single quantitiy lnx+ lny-ln5 (answered by stanbon)

How do you write this as a single logarithm of a single argument 1/2*ln5+3*ln2... (answered by stanbon)

Solve the following equation for x: {{{ ln(ln(x-3)) + ln(2) = ln5... (answered by Alan3354)

6. use the change base formula to write the logarithm as a multiple of a common log.... (answered by vleith)

e^ln5 (answered by ewatrrr)

how do you make this a single logarithm? ln5 +... (answered by Edwin McCravy)

3 lns that when subtracted, make ln5. How Can I Determine The 3... (answered by Alan3354)

Suppose that ln5=p and ln6=q. Use properties of logarithms to write the logarithm in... (answered by greenestamps)