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Question 1 of 3
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Expand the fraction by transforming it into a difference
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logaxyzlogaxyz |
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== |
logaxy−logazlogaxy−logaz |
Expand the first term by transforming it into a sum
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logaxy−logazlogaxy−logaz |
== |
logax+logay−logazlogax+logay−logaz |
logax+logay−logazlogax+logay−logaz
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Question 2 of 3
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logax√x+4logax√x+4
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Expand the expression by transforming it into a sum
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logax√x+4logax√x+4 |
== |
logax+loga√x+4logax+loga√x+4 |
Expand further by using the following laws
logbxplogbxp |
== |
plogbxplogbx |
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logax+loga√x+4logax+loga√x+4 |
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== |
logax+loga(x+4)12logax+loga(x+4)12 |
Change the surd into an exponent |
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logax+logax+ 1212loga(x+4)loga(x+4) |
logbxp=plogbxlogbxp=plogbx |
logax+12loga(x+4)logax+12loga(x+4)
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Question 3 of 3
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logax(y+z)a3logax(y+z)a3
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Expand the fraction by transforming it into a difference
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logax(y+z)a3logax(y+z)a3 |
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== |
logax(y+z)−logaa3logax(y+z)−logaa3 |
Expand the first term by transforming it into a sum
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logax(y+z)−logaa3logax(y+z)−logaa3 |
== |
logax+loga(y+z)−logaa3logax+loga(y+z)−logaa3 |
Expand further by using the following laws
logbxplogbxp |
== |
plogbxplogbx |
logbblogbb |
== |
11 |
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logax+loga(y+z)-logaa3logax+loga(y+z)−logaa3 |
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logax+loga(y+z)-logax+loga(y+z)− 33logaalogaa |
logbxp=plogbxlogbxp=plogbx |
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logax+loga(y+z)-3(logax+loga(y+z)−3(11)) |
logbb=1logbb=1 |
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logax+loga(y+z)-3logax+loga(y+z)−3 |
logax+loga(y+z)-3logax+loga(y+z)−3