how do i find the value of x of this logarithm as a decimal?
4^x - 3 = 25
2007-05-12 09:41:42 · 7 answers · asked by rolie p 1 in Science & Mathematics ➔ Mathematics
simplify: 4^x = 28
take natural log of both sides: ln(4^x) = ln(28)
simplify using rules of logs: x*ln(4) = ln(28)
solve for x: x = ln(28) / ln(4) = 2.40
2007-05-12 09:44:05 · answer #1 · answered by Matt 3 · 0⤊ 0⤋
Alright so first try to solve further. Add 3 to both sides. Now you have 4^x=28
Now, 4 to the what power=28?
I did this by guess n check hehe.
4^2=16
4^3=64
(therefore, it is between 2 and 3)
The answer is x=2.4
4^2.4=27.858
4^2.4=28
2007-05-12 16:51:27 · answer #2 · answered by acmbeauty 2 · 0⤊ 0⤋
In the form :
4^x - 3 = 25
4^x = 28
Taking log of two sides
x log 4 = log 28
x= log 28 / log 4
x= 2.403677461
In the form :
4^(x-3) = 25
Taking log of two sides
(x-3) log 4 = log 25
x-3 = log 25/log 4 =2.321928095
x= 5.321928095
2007-05-12 16:52:58 · answer #3 · answered by a_ebnlhaitham 6 · 0⤊ 0⤋
This boils down to 4^x = 28 or exp(x ln(4)) = 28 which is equivalent to: x ln(4) = ln(28) = ln(4) + ln(7). Therefore:
x = 1 + ln(7)/ln(4) = 2.403677461...
2007-05-12 16:50:46 · answer #4 · answered by DrGerard 5 · 0⤊ 0⤋
4^x - 3 = 25
4^x = 28
x ln 4 = ln 28
x = (ln 28)/(ln 4) = 3.332/1.386
x = 2.40
.
2007-05-12 16:48:21 · answer #5 · answered by Robert L 7 · 0⤊ 0⤋
add the three to the right side of the equation like normal algebra. Divide the right side by the four, and hit your log key. You should get something less than one.
2007-05-12 16:46:53 · answer #6 · answered by buckhomes 2 · 0⤊ 2⤋
ln28/ln4
= 2.40
2007-05-12 16:49:29 · answer #7 · answered by over the air 3 · 0⤊ 0⤋