Today in class, we learned how to apply the Change of Base Formula of logarithms. It was so very fun. We also learned how to solve logarithmic and exponential equations when bases are different. That was a blast as well. 

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Here is some of the easier stuff first…

log89= log 9/log 8

When you type that into the calculator you put in…

log(9) / log(8) 

Make sure you have the parenthesis! 

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Now the harder stuff…

2^4x-1 = 3^1-x

1) Bring the parenthesis down in front

 

2) Apply (log) to each of the numbers

It should look like this…

(4x-1)(log2)=(1-x)(log3)

3) Next, Distribute

4x(log2) - 1(log2) = 1(log3) -x(log3)

4) Then, combine the like terms

4x(log2) + x(log3) = log3 + log2

5) After that, factor out the x

x (4log2 + log3) = log3 + log2

6) Divide to get the x by itself (use calculator)

x = log3 + log2 / 4log2 + log3

7) The answer should be x= .977!

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