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# Logarithm - Algebra

+5
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0.65=100(0.5)^(t/418)

what is t?

OhMyBeni  Feb 21, 2017

#5
+16
+5

CPhil - thank you I think im understanding better now.

Guest user - no I litereally said that i dont work with math. Maybe you cant read? also the "negatives" are just bad formating on my part. They arent negatives. They are indents.

OhMyBeni  Feb 21, 2017
#1
+10

solve 0.65 = 100×0.5^(t/418) for t, divide both sides by 100

0.0065 = 0.5^(t/418) Take the log of sides

t/418 =Log(0.0065) / Log(0.5)

t/418 =7.265345..... cross multiply

t = 3,036.914

Guest Feb 21, 2017
#2
+16
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Thank you for the quick reply, but im not understanding.

These were my results, so where did I go wrong? Im not a mathmetician and i am not taking any courses, my coworker wanted to know if i could solve this.

Q. 0.65 = 100 x 0.5^x (t÷418)

- 0.65=100 x 0.5 x t/418 - reduce with greatest common divisor 2

- 0.65=50 x 5/10 x t/418 - reduce numbers with 10

- 0.65/1 x 25t/209 -calculate

- 0.65 = 25t/209 - cross mulitply

- 0.65/1 x 25t/209

- 0.65 x 209 = 1 x 25t

- 135.85 = 25t - Switch Sides of equation

- 25t = 135.85 - divide both sides by 25

- 25 ÷ 135.85 = 5.434

A. T = 5.434

Note - my dash symbolizes a fraction. Ex. "1 over 2"

OhMyBeni  Feb 21, 2017
#3
+5

You can only solve this by using "Logs", which you don't seem to have that much understanding of them. Everything after the first line is wrong!. This: 0.5^(t/418) is quite DIFFERENT from: 0.5 x t/418!!.

Also, why did you turn 0.65 into NEGATIVE -0.65???. You cannot take the Log of a negative number!.

Guest Feb 21, 2017
#4
+87334
+5

Remember that  (t/418) is an exponent....we can't just bring it down as a multiplier

Note the difference  ......     3^2  = 9   ....but....   3 * 2   = 6  ......not the same!!!!

0.65=100(0.5)^(t/418)    it's easiest to divide everything by 100, first

.65  / 100  = (1/2)^(t/418)

.0065  = (1/2)^(t/418)     we heve an exponent....to get rid of this, take the log of both sides

log (.0065)  = log(1/2)^(t/418)

We have a property that says that     log (a)^b  = b *log (a)

So....we can bring the exponent out front of the log as a multiplier

log (.0065)  =  (t/418) * log(1/2)     divide by  log (1/2) on both sides

log (.0065) / log (1/2)  =  t /418     mutliply  both sides by 418

418 * log (.0065) / log (1/2)  =   t  ≈ 3036.914

CPhill  Feb 21, 2017
#5
+16
+5

CPhil - thank you I think im understanding better now.

Guest user - no I litereally said that i dont work with math. Maybe you cant read? also the "negatives" are just bad formating on my part. They arent negatives. They are indents.

OhMyBeni  Feb 21, 2017