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
+16 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"
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!.
+128406 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
