Final answer:
To solve the equation 27^(3x) = 81^(x+10), we can express both numbers in terms of a common base and equate the exponents. By simplifying the equation and solving for x, we find that x = 8.
Step-by-step explanation:
To solve the equation 27^(3x) = 81^(x+10), we can express both numbers in terms of a common base. Both 27 and 81 can be written as powers of 3, since 3^3 = 27 and 3^4 = 81. So, we have (3^3)^(3x) = (3^4)^(x+10). Applying the power of a power rule, we get 3^(9x) = 3^(4x+40).
For the two sides to be equal, the exponents must be equal. So, we have the equation 9x = 4x + 40. Subtracting 4x from both sides, we get 5x = 40. Finally, dividing both sides by 5, we find that x = 8.
Therefore, the value of x that satisfies the equation is 8.