WhAt is x

3x9^x=81

I assume the left reads three times nine to the x power.

3*9^x=3*3^2x=3^(2x+1)

3^(2x+1)=81
take the log base three of both sides.

2x+1=4
2x=3
x=1.5

weird problem

or

3x9^x=81 , divide both sides by 3
9^x= 27
(3^2)^x = 3^3
3^(2x) = 3^3
2x = 3
x = 3/2 = 1.5

To find the value of x in the equation 3x * 9^x = 81, we can solve it step by step:

Step 1: Simplify the equation:
Rewrite 81 as 9^2, since 9^2 equals 81.

3x * 9^x = 9^2

Step 2: Use the property of exponents:
Since the bases are the same (9), the exponents can be equated:

3x = 2

Step 3: Solve for x:
Divide both sides of the equation by 3:

3x/3 = 2/3

x = 2/3

Thus, the value of x in the equation 3x * 9^x = 81 is x = 2/3.

To solve the equation 3x * 9^x = 81, we can start by simplifying the equation. Firstly, we can rewrite 9^x as (3^2)^x and apply the exponent rule: (a^m)^n = a^(m*n). So, 9^x becomes 3^(2x).

Now, substituting this back into the equation, we have 3x * 3^(2x) = 81. Since both terms have the same base (3), we can combine them using the multiplication rule: a^m * a^n = a^(m+n). Thus, we get 3^(x+2x) = 81, which simplifies to 3^(3x) = 81.

Since both sides of the equation have the same base (3), we can express 81 as a power of 3: 81 = 3^4. Hence, 3^(3x) = 3^4. We can now apply the rule that if two powers with the same base are equal, then their exponents must be equal as well. Therefore, we have 3x = 4.

To solve for x, divide both sides of the equation by 3: x = 4/3.

Thus, the value of x that satisfies the equation 3x * 9^x = 81 is x = 4/3.