CONDENSING(MARIA)

CONDENSING

Condense: Make (something) denser or more concentrated Helpful Tip:  think of condensing like simplifying logs

Example 1 log2( 5 ) - log2( x ) + log2( 8 ) Log2(40) – log2( x )  Log2(40/ x )

__step__ 1: if the logs are addition then you can multiply them  5 x 8 = 40

step 2: - if the logs are subtraction then you can divide - because we already multiplied 5 x 8, we now have to divide the remaining so

40/x

<span style="display: block; font-family: Impact,Charcoal,sans-serif; font-size: 170%; text-align: center;">Example 2 <span style="display: block; font-family: Impact,Charcoal,sans-serif; font-size: 170%; text-align: center;"> <span style="color: #e2286e; font-family: Impact,Charcoal,sans-serif; font-size: 340%;">log2(x) <span style="font-family: Impact,Charcoal,sans-serif; font-size: 340%;">- <span style="color: #5b891f; font-family: Impact,Charcoal,sans-serif; font-size: 340%;">3log3(y) <span style="font-family: Impact,Charcoal,sans-serif; font-size: 340%;"> + <span style="color: #e2286e; font-family: Impact,Charcoal,sans-serif; font-size: 340%;">4log2(z) <span style="font-family: Impact,Charcoal,sans-serif; font-size: 340%;"> - <span style="color: #5b891f; font-family: Impact,Charcoal,sans-serif; font-size: 340%;">log3(4)^2

<span style="color: #e2286e; font-family: Impact,Charcoal,sans-serif; font-size: 340%;">log2(x) <span style="font-family: Impact,Charcoal,sans-serif; font-size: 340%;">+ <span style="color: #e2286e; font-family: Impact,Charcoal,sans-serif; font-size: 340%;">4log2(z) <span style="font-family: Impact,Charcoal,sans-serif; font-size: 340%;"> - <span style="color: #5b891f; font-family: Impact,Charcoal,sans-serif; font-size: 340%;">3log3(y) - log3(4)^2 <span style="color: #e2286e; font-family: Impact,Charcoal,sans-serif; font-size: 44px; line-height: 66px;">log2(XZ^4) <span style="color: #000000; font-family: Impact,Charcoal,sans-serif; font-size: 44px; line-height: 66px;">- <span style="color: #5b891f; font-family: Impact,Charcoal,sans-serif; font-size: 44px; line-height: 66px;">log3(y^3) - log3(16)  <span style="color: #e2286e; font-family: Impact,Charcoal,sans-serif; font-size: 44px; line-height: 66px;">log2(XZ^4) - <span style="color: #5b891f; font-family: Impact,Charcoal,sans-serif; font-size: 44px; line-height: 66px;"> log3(y^3 x 16)  <span style="color: #000000; font-family: Impact,Charcoal,sans-serif; font-size: 44px; line-height: 66px;">log2(XZ^4) - log3(y^3 x 16)

<span style="display: block; font-family: Impact,Charcoal,sans-serif; font-size: 22px; text-align: center;">STEP 1:add or subtract the logs with the same basepink has the same base of 2and green has the same base of 3 <span style="display: block; font-family: Impact,Charcoal,sans-serif; font-size: 22px; text-align: center;"> <span style="display: block; font-family: Impact,Charcoal,sans-serif; font-size: 22px; text-align: center;">__STEP__ 2: <span style="display: block; font-family: Impact,Charcoal,sans-serif; font-size: 22px; text-align: center;">-notice how there is a number in front of some of the bases, with that you simply take the number that is in front and put it as an exponent <span style="display: block; font-family: Impact,Charcoal,sans-serif; font-size: 22px; text-align: center;">-combine the like terms for each of the two different bases <span style="display: block; font-family: Impact,Charcoal,sans-serif; font-size: 22px; text-align: center;">so <span style="color: #e2286e; font-family: Impact,Charcoal,sans-serif; font-size: 22px;">(x) times <span style="color: #e2286e; font-family: Impact,Charcoal,sans-serif; font-size: 22px;">z to the 4th power <span style="display: block; font-family: Impact,Charcoal,sans-serif; font-size: 22px; text-align: center;">-now do the same step for the green part <span style="display: block; font-family: Impact,Charcoal,sans-serif; font-size: 22px; text-align: center;"> <span style="display: block; font-family: Impact,Charcoal,sans-serif; font-size: 22px; text-align: center;">

<span style="display: block; font-family: Impact,Charcoal,sans-serif; font-size: 22px; text-align: center;">EXAMPLE 3 <span style="display: block; font-family: Impact,Charcoal,sans-serif; font-size: 22px; text-align: center;"> media type="youtube" key="UR126niUo6c?rel=0" height="315" width="420" align="center" <span style="display: block; font-family: Impact,Charcoal,sans-serif; font-size: 22px; text-align: center;"> <span style="font-family: Impact,Charcoal,sans-serif;"> this is another example of having a number in front of the log and turning it into an exponent. <span style="display: block; font-family: Impact,Charcoal,sans-serif; font-size: 170%; text-align: center;"> <span style="display: block; font-family: Impact,Charcoal,sans-serif; font-size: 170%; text-align: center;"> <span style="display: block; font-family: Impact,Charcoal,sans-serif; font-size: 170%; text-align: center;">