how do you solve 27 - 3^5x * 9^x2
sorry it is 27= 3^5x x 9^x2
3^3 = 3^(5x) * [(3^2)^(x^2)] = 3^(2 x^2 + 5 x)
2 x^2 + 5 x - 3 = 0 ... (2 x - 1) (x + 3) = 0
x = 1/2 , x = -3
To solve the expression 27 - 3^5x * 9^x2, we can follow the order of operations, which states that we should first perform any calculations inside parentheses, then exponents, then multiplication and division (from left to right), and finally addition and subtraction (from left to right).
Looking at the expression, there are no parentheses. Next, we notice that we have exponents.
To simplify the expression, let's separate the two terms involving exponents: 3^5x and 9^x2.
Starting with 3^5x, we can rewrite it as (3^5)^x since the exponent applies to both the 3 and the 5:
(3^5)^x * 9^x2
Next, we can simplify 3^5, which is equal to 243:
243^x * 9^x2
Now let's focus on the second term, 9^x2. Notice that 9 can be expressed as 3^2:
243^x * (3^2)^x2
We can simplify the expression within the parenthesis:
243^x * 3^(2x2)
Simplifying further:
243^x * 3^(4x)
Finally, we can apply the rule that states when raising a power to another power, we multiply the exponents:
(3^5)^x * 3^(4x)
Now we can simplify both terms:
3^(5x) * 3^(4x)
When multiplying two exponents with the same base, we add the exponents:
3^(5x + 4x)
This simplifies to:
3^(9x)
Therefore, the simplified expression is 3^(9x).