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# Logarithm help watch

any assistant would be greatly appreciated.

Solve:
log_x(x+6)=2

log_3x-3(log_3y+2log_3z)

log x + log(x-15)=2

2^2x-3*2^x-40=0

log_4x+log_8x=5

also, anyone good with story problems? here's one.
you invest \$2000 in an acct that pays 4.3% interest compounded continuously, find to the nearest tenth of a yr when the acct will be worth \$10K.
2. The first one goes like this:

log_x(x + 6) = 2
=> x^2 = x + 6
x^2 - x - 6 = 0
(x+2)(x-3) = 0
x = -2 , 3
3. For the last one:

log_8 x=1/3 log_2 x
log_4 x=1/2 log_2 x
=> log_8 x +log_4 x=1/3 log_2 x +1/2 log_2 x=5/6 log_2 x
=> 5/6 log_2 x= 5
=> log_2 x = 6
=> x=2^6=64, which fits
4. Not sure about number 2 but:
log_3 x -3log_3 y -6log_3 z=log_3 x -log_3 y^3 -log_3 z^6
=log_3(x/(y^3*z^6))

3:
log x + log(x-15)=log x(x-15)
log x(x-15)=2
=> 10^2=x(x-15)
x^2-15x=100
=>x^2-15x-100=0
=>(x-20)(x+5)=0
=>x=-5 or 20
However, 10^x=-5 has no real solutions since x<0. Therefore, x=20.

4:
2^2x-3*2^x-40=(2^x-1.5)^2-42.25 (completing the square)
=>(2^x-1.5)^2=42.25
=>2^x-1.5=+6.5
=>2^x=8 or -5
As 2^x=-5 has no solutions, 2^x=8
Therefore, x=3
5. And the wordy one:

If v is value and y is years:

v=2000*1.043^y
When v=10000:
10000=2000*1.043^y
5=1.043^y
ln 5=ln 1.043^y
ln 5=y ln 1.043
y=ln 5/ln 1.043
y= 38.2278...years
=38.2 years (to 1dp)

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Updated: December 8, 2003
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