# do a 12 question quiz for me (ALGEBRA 2) (LOG)

**Question description**

i will provide my user info, and also inform you the LOG :

ometimes to simplify or evaluate logarithms you need to change the base. This is very straight forward.

log_{a}b = (log b)/(log a) = (ln b)/(ln a)

So log_{2}5 = log 5/log2 or = ln 5/ln2

Sometimes you will need to use change an exponential equation into the equivalent logarithmic equation and then use change of base to solve.

5^{2x}= 28

log_{5} 28 = 2x

x = (1/2) log_{5} 28 = (1/2) log 28/log 5

What do you do when you have two exponentials equal to one another with variables in both exponents? Use the same approach

2^{x+2} = 3^{x}

log_{2} 3^{x} = x+2

x log_{2} 3 = x+2

x (log_{2} 3 – 1) = 2

x = 2/( log_{2} 3 – 1) = 2/[(log 3/log 2) – 1] = 3.419

On the quiz you will likely have a word problem. If it asks about hydronium ion, it is represented as H_{3}O^{+}.

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