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The first type of logarithmic equation has two logs, each having the same base, set equal to each other, and you solve by setting the insides (the "arguments") equal to each other.
For example:
- Solve log2(x) = log2(14).
Since the logarithms on either side of the equation have the same base ("2", in this case), then the only way these two logs can be equal is for their arguments to be equal. In other words, the log expressions being equal says that the arguments must be equal, so I have:
x = 14
And that's the solution: x = 14
- Solve logb(x2) = logb(2x - 1).
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Since the bases of the logs are the same (the unknown value "b", in this case), then the insides must be equal. That is:
x2 = 2x - 1
Then I can solve the log equation by solving this quadratic equation:
x2 - 2x + 1 = 0
(x - 1)(x - 1) = 0
Then the solution is x = 1.
Logarithms cannot have non-positive arguments, but quadratics and other equations can have negative solutions. So it is generally a good idea to check the solutions you get for log equations:
logb(x2) = logb(2x - 1)
logb([1]2) ?=? logb(2[1] - 1)
logb(1) ?=? logb(2 - 1)
logb(1) = logb(1)
The value of the base of the log is irrelevant here. Each log has the same base, each log ends up with the same argument, and that argument is a positive value, so the solution "checks".
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How do you solve log x - 2?
You cannot solve log x- 2 unless (i) log x - 2 is equal to some number or (ii) x is equal to some number.
Log x plus log 2 equals log 2?
log(x) + log(2) = log(2)Subtract log(2) from each side:log(x) = 0x = 100 = 1
How do you solve 3 to the power of negative 2x plus 2 equals 81?
3^(-2x + 2) = 81? log(3^(-2x + 2)) = log(81) (-2x+2)log(3) = log(81) -2x = log(81)/log(3) - 2 x = (-1/2)(log(81)/log(3)) + 1
How do you solve 5 - x -3?
8
What does x equals in 2 log x equals log 8?
2 log(x) = log(8)log(x2) = log(8)x2 = 8x = sqrt(8) = 2.82843 (rounded)Note that only the positive square root of 8 can serve as a solution to thegiven equation, since there's no such thing as the log of a negative number.
Solve for x log 9 x equals 2?
log9(x)=2 x=9^2 x=81
How do you solve log x plus 2 equals log 9?
log x + 2 = log 9 log x - log 9 = -2 log (x/9) = -2 x/9 = 10^(-2) x/9 = 1/10^2 x/9 = 1/100 x= 9/100 x=.09
How do you solve for X in Log x plus 9 - Log x equals 2?
11
How do you solve 2logx plus 3logx equals 10?
2 log(x) + 3 log(x) = 105 log(x) = 10log(x) = 10/5 = 210log(x) = (10)2x = 100
How do you solve log x - 2?
You cannot solve log x- 2 unless (i) log x - 2 is equal to some number or (ii) x is equal to some number.
How do you solve 3 log of 8 equals x?
x = 3*log8 = log(83) = log(512) = 2.7093 (approx)
Why is the answer for log x squared equals 2 different than 2log x equals 2?
log x2 = 2 is the same as 2 log x = 2 (from the properties of logarithms), and this is true for x = 10, because log x2 = 2 2 log x = 2 log x = 1 log10 x = 1 x = 101 x = 10 (check)
Log x plus log 2 equals log 2?
log(x) + log(2) = log(2)Subtract log(2) from each side:log(x) = 0x = 100 = 1
How do you solve log base 2 of x - 3 log base 2 of 5 equals 2 log base 2 of 10?
[log2 (x - 3)](log2 5) = 2log2 10 log2 (x - 3) = 2log2 10/log2 5 log2 (x - 3) = 2(log 10/log 2)/(log5/log 2) log2 (x - 3) = 2(log 10/log 5) log2 (x - 3) = 2(1/log 5) log2 (x - 3) = 2/log 5 x - 3 = 22/log x = 3 + 22/log 5
How do you solve 3 to the power of negative 2x plus 2 equals 81?
3^(-2x + 2) = 81? log(3^(-2x + 2)) = log(81) (-2x+2)log(3) = log(81) -2x = log(81)/log(3) - 2 x = (-1/2)(log(81)/log(3)) + 1
What s the G of x if it equals log 2 x plus 2?
G(x) = log(2x) + 2, obviously!
What is the value of x if log base 10 of x equals 2?
Logs to base 10 are common logs and are abbreviated to lg; to solve use antilogs: lg x = 2 → 10^(lg x) = 10^2 → x = 10² = 100
