Logarithm Equation

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June 28th 2006, 09:34 AM
coopsterdude

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Logarithm Equation

Hi, can you please help me to understand a portion of this example. I am ok until the 4th line that uses the distributive property. Should I distribute the ln alone or do I distribute the ln 2?

Again, it’s line 4 that I have a problem understanding. I think I could figure out the rest once I understand line 4.

Thanks for your help with this one.
June 28th 2006, 11:02 AM
Soroban

Hello, coopsterdude!

Quote:

Can you please help me to understand a portion of this example?
I am ok until the 4th line that uses the distributive property.
Should I distribute the ln alone or do I distribute the ln 2?

$2^{2x-1} \;= \;3^x$

$\ln(2^{2x-1}) \;= \;\ln(3^x)$

$(2x - 1)\cdot\ln 2 \;= \;x\cdot\ln 3$

$2x\cdot\ln 2 - \ln 2 \;= \;x\cdot\ln 3$ . . . Distributive Property

Don't you see anything wrong with this?

. . $(2x - 1)\cdot\ln 2 \;= \;(2x\cdot\ln - \ln)\cdot 2$

Think about what you're asking . . .

If I have: . $(x + 7)\cdot\sqrt{3}$ ,

. . can I distribute the $\sqrt{\;\;}$ and leave the $3$ outside

. . and get: . $(x\sqrt{\;\;} + 7\sqrt{\;\;})\cdot3$ ?

Oh, sure . . . why not?
June 28th 2006, 02:18 PM
coopsterdude

Thanks Soroban, that's how I would have done the distribution. Isolating the x in that way led to my confusion. Thanks for you help.