log3(7x+6)-log94x(squared)=1

ey-1=6/e

ln x2 +ey=18, find the value of (square root)ey(ln x3)

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- Mar 15th 2008, 06:55 AMtyana21Logarithmic and exponential function questions
log3(7x+6)-log94x(squared)=1

ey-1=6/e

ln x2 +ey=18, find the value of (square root)ey(ln x3) - Mar 15th 2008, 07:26 AMPeritus

----------------------------------------------------------- - Mar 15th 2008, 07:47 AMMoo
Hello,

But we know that

So, as 4x² = (2x)², \ln(4x²)=2 \ln(2x) and as 9 = 3², \ln(9) = 2 \ln(3)

Hence

But ln(a)-ln(b)=ln(a/b)

<=>

You'll just have to study the values of x for which the equation can't be solved. - Mar 15th 2008, 10:48 AMSoroban
Hello, tyana21!

An I reading the first one correctly?

Quote:

The first log can be written: . .******

The second can be written: .

The equation becomes: .

Divide by 2: .

Then we have: .

Exponentiate: .

Therefore: .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

******

Let

Then: .

Take logs, base 9: .

Since , we have: .

Therefore: .

- Mar 16th 2008, 05:04 AMtyana21
yes you read it correctly.im a newbie so i have no idea how to write it out since i was in a rush.

- Mar 16th 2008, 05:40 AMMoo
So don't bother with my message, because i read

:p - Mar 16th 2008, 06:22 AMtyana21