these are some problems i do not get any help is appreciated. These are copied exactly from the worksheet so i don't think i wrote anything wrong. Please explain it for me and could i get the answer thanks (:
Log7 x= ½ log7 36 (log base 7)
log x=2log 5+ log 4
Logx 10 + logx 8-logx 5= 4 (log base x)
5^2x=3
Log7 x= ½ log7 36 (log base 7)
log7 (x) = log7 (36)^.5
so
x = 36^.5 = 6
log x=2log 5+ log 4
log x = log(5)^2 + log 4
log x = log (25*4)
x = 100
Logx 10 + logx 8-logx 5= 4 (log base x)
logx (10*8/5) = 4
logx (16) = 4
16 = x^4
well, what to the fourth power = 16 ?
5^2x=3
2 x log 5 = log 3
x log 25 = log 3
x = log 3 / log 25
i have this problem ½ log2 x=3log22-log24
(log base 2) it is kinda of the same as the first one but i don't undersand how you got them?
log2 (x^.5 ) = log2 (8) - log2(4)
log2 (x^.5) = log2 (2) which is 1
log 2 (x^.5) = 1
x^.5 = 2^1 = 2
x = 2^2 = 4
Certainly! I'll explain how to solve each of these problems step by step.
1. Log7 x = ½ log7 36:
To solve this equation, you can use the logarithmic property that states log_b (a^m) = m * log_b (a).
First, rewrite the equation using the property mentioned above:
log7 x = log7 (36^(1/2))
Since the base of the logarithm is the same (log base 7), the argument inside the logarithm must be equal. Therefore, x = 36^(1/2).
Now, calculate the square root of 36, which is 6. So, x = 6 would be the solution to this equation.
2. log x = 2log 5 + log 4:
This equation involves logarithms with different bases. We need to use the change of base formula to rewrite the logarithms with a common base, such as log base 10 or log base e.
Using the change of base formula, we can rewrite the equation as:
log x = (log 5^2) / (log 10) + (log 4) / (log 10)
Simplify the equation:
log x = 2(log 5) / (log 10) + (log 4) / (log 10)
Now, solve for each logarithm and simplify further:
log x = (2 * 0.69897) / 1 + 0.60206 / 1
log x = 1.39794 + 0.60206
log x = 1.999
To get rid of the logarithm, we need to convert it back to exponential form. Therefore, x = 10^1.999.
Evaluating the expression, x = 99.949.
3. Logx 10 + logx 8 - logx 5 = 4 (log base x):
This equation involves logarithms with the same base, which is log base x. We can use the logarithmic property log_a (x * y) = log_a(x) + log_a(y) and log_a (x / y) = log_a(x) - log_a(y).
Using these properties, we can rewrite the equation as:
logx (10 * 8 / 5) = 4
Simplifying the expression inside the logarithm:
logx (16) = 4
Converting the logarithmic equation to exponential form, we have:
x^4 = 16
Taking the fourth root of both sides, we find:
x = ±√(16)
So, the possible solutions for x are x = 2 or x = -2.
4. 5^(2x) = 3:
To solve this exponential equation, we need to take the logarithm of both sides. You can choose any base for the logarithm, but a common choice is the natural logarithm (log base e).
Taking the natural logarithm (ln) of both sides, we have:
ln (5^(2x)) = ln 3
Using the property log_a (a^x) = x, we get:
2x * ln 5 = ln 3
Now, solve for x by isolating it:
2x = ln 3 / ln 5
Divide both sides by 2 to get the value of x:
x = (ln 3 / ln 5) / 2
Evaluate further using a calculator if needed.