Answer:
x = 30517578124/29296875
Step-by-step explanation:
Solve for x:
3125 = 3 x + 1/9765625
Put each term in 3 x + 1/9765625 over the common denominator 9765625: 3 x + 1/9765625 = (29296875 x)/9765625 + 1/9765625:
3125 = (29296875 x)/9765625 + 1/9765625
(29296875 x)/9765625 + 1/9765625 = (29296875 x + 1)/9765625:
3125 = (29296875 x + 1)/9765625
3125 = (29296875 x + 1)/9765625 is equivalent to (29296875 x + 1)/9765625 = 3125:
(29296875 x + 1)/9765625 = 3125
Multiply both sides of (29296875 x + 1)/9765625 = 3125 by 9765625:
(9765625 (29296875 x + 1))/9765625 = 9765625×3125
(9765625 (29296875 x + 1))/9765625 = 9765625/9765625×(29296875 x + 1) = 29296875 x + 1:
29296875 x + 1 = 9765625×3125
9765625×3125 = 30517578125:
29296875 x + 1 = 30517578125
Subtract 1 from both sides:
29296875 x + (1 - 1) = 30517578125 - 1
1 - 1 = 0:
29296875 x = 30517578125 - 1
30517578125 - 1 = 30517578124:
29296875 x = 30517578124
Divide both sides of 29296875 x = 30517578124 by 29296875:
(29296875 x)/29296875 = 30517578124/29296875
29296875/29296875 = 1:
Answer: x = 30517578124/29296875
For this case:
We rewrite the equation as:
[tex]5 ^ {- 10 + 3x} = 3.125[/tex]
We find ln on both sides of the equation to remove the exponent variable:
[tex]ln (5 ^ {- 10 + 3x}) = ln (3,125)[/tex]
Applying properties of logarithm we have:
[tex](-10 + 3x) ln (5) = ln (3.125)[/tex]
We apply distributive property:
[tex]-10ln (5) + 3xln (5) = ln (3,125)[/tex]
We clear the value of "x":
[tex]3xln (5) = ln (3,125) + 10ln (5)\\x = \frac {ln (3.125)} {3ln (5)} + \frac {10ln (5)} {3ln (5)}\\x = \frac {ln (3.125)} {3ln (5)} + \frac {10} {3}[/tex]
ANswer:
[tex]x = \frac {ln (3.125)} {3ln (5)} + \frac {10} {3}[/tex]
