who ever will help me I do not understand this problem?
Solve each exponential. Give the exact value of x
6^x = 1/36
3^x = 8
I really do not understand at all I have not taken algebra since 8th grade and went back to school at 67, Thank you if you wish to help me understand how to do these problem it is appreciated.
6^x = (1/6)^2
6^x = 6^-2
x = -2
3^x = 8
Log3^x = log8
x log3 = log8
x = log8/log3
Take the natural log (Ln) of each side of the equation to isolate the variable.
Ln(6^x)=Ln(1/36)
x*Ln(6)=Ln(1/36)
Solve for x:
x=Ln(1/36)/Ln(6)
The other problem is exactly the same.
thank you for your help. I am feeling like I don't have a brain at all. I work on these homework problems from 9 to 3 this morning. Thanks again I really do appreciate it greatly.
Of course, I'm here to help you understand how to solve these exponential equations step by step.
Let's start with the first equation: 6^x = 1/36.
To solve this equation, we need to rewrite both sides of the equation with the same base. In this case, we can rewrite 1/36 as 6^(-2) since 1/6^2 is equal to 1/36.
So now our equation becomes 6^x = 6^(-2).
Since the bases are the same, we know that the exponents must be equal. Therefore, we can say that x = -2.
So the exact value of x in the equation 6^x = 1/36 is x = -2.
Now let's move on to the second equation: 3^x = 8.
To solve this equation, we need to rewrite 8 with a base of 3. We can write 8 as 2^3 since 2 x 2 x 2 = 8.
So now our equation becomes 3^x = 2^3.
Again, since the bases are different, we need to find a way to rewrite the equation with the same base. In this case, both 3 and 2 can be expressed as powers of the same base, which is 2.
So let's rewrite the equation using the base 2:
(2^1)^x = 2^3.
Now, we can apply the power rule of exponents, which states that when we raise an exponent to another exponent, we multiply the exponents:
2^(1 * x) = 2^3.
Now, since the bases are the same, we can equate the exponents:
1 * x = 3.
Therefore, x = 3.
So the exact value of x in the equation 3^x = 8 is x = 3.
I hope this explanation helps you understand how to solve these exponential equations. If you have any further questions, please feel free to ask.