Where appropriate, include the approximation to the nearest ten-thousandth.
24.) 3^x= 1/81
25.) logx 125 =3
26.) log64 x = 1/2
These are extraordinarily easy. For instance, what is 5 cubed?
I will be happy to critique your thinking.
Where appropriate, include the approximation to the nearest ten-thousandth.
24.) 3^x= 1/81 I have x = 1/5
25.) logx 125 =3 I have x = 5
26.) log64 x = 1/2 I have x = 8
Are these answers right?
Where appropriate, include the approximation to the nearest ten-thousandth.
24.) 3^x= 1/81 I have x = 1/5
25.) logx 125 =3 I have x = 5
26.) log64 x = 1/2 I have x = 8
Are these answers right?
on the first, log3 of each side
x= -log3 81=-4
others are right.
Thanks
To solve these equations and find the values of x, you need to apply the appropriate mathematical properties and techniques. Let's go through each equation step by step:
24.) 3^x = 1/81
To solve this equation, we need to express both sides of the equation with the same base. Since 3 can be written as 3^2, we can rewrite the equation as:
3^2x = 1/81
Now, we can express 1/81 as 3^(-4):
3^2x = 3^(-4)
Now, since both sides of the equation have the same base, the exponents must also be equal:
2x = -4
To isolate x, divide both sides of the equation by 2:
x = -4/2
Simplifying, we have:
x = -2
Therefore, the solution to the equation is x = -2.
25.) logx 125 = 3
To solve this equation, we need to rewrite it in exponential form. The logarithm equation logx y = z is equivalent to x^z = y.
So, we can rewrite the given equation as:
x^3 = 125
Since 125 is equal to 5^3, we can further simplify the equation as:
x^3 = 5^3
Now, we have the same base on both sides, so the exponents must be equal:
x = 5
Therefore, the solution to the equation is x = 5.
26.) log64 x = 1/2
Similar to the previous equation, we need to rewrite this equation in exponential form. The logarithm equation logx y = z is equivalent to x^z = y.
So, we can rewrite the equation as:
64^(1/2) = x
Simplifying the left side, we have:
√64 = x
√64 = ±8
Since we are looking for the positive square root, we have:
x = 8
Therefore, the solution to the equation is x = 8.