Question

What is the expression for f(x) when we rewrite 3^5x+3 • 27^x as 3^f(x)?

f(x)=

Answer 1

To rewrite 3^5x+3 • 27^x as 3^f(x), we need to express the given expression using only powers of 3. After simplifying the expression and combining like terms, we find that f(x) = 8x+3.

Step-by-step explanation:

To rewrite 3^5x+3 • 27^x as 3^f(x), we need to express the given expression using only powers of 3. Let's break it down step by step:

1. Since 27 is equal to 3^3, we can rewrite the expression as: 3^5x+3 • (3^3)^x.
2. By applying the power of a power rule, we can simplify it further: 3^5x+3 • 3^(3x).
3. Now, using the multiplication rule for exponents, we can combine the terms with the same base: 3^(5x+3+3x).

Finally, we can simplify the exponent: 5x+3+3x = 8x+3. Therefore, the expression is f(x) = 8x+3.

Answer 2

To rewrite the expression 3^(5x+3) • 27^x as 3^f(x), we can use the fact that 27 can be written as 3^3. Then, we have:

3^(5x+3) • 27^x
= 3^(5x+3) • (3^3)^x [replace 27 with 3^3]
= 3^(5x+3) • 3^(3x) [simplify the exponent of 3]
= 3^(5x+3+3x) [combine the bases by adding the exponents]

Therefore, we can rewrite the expression as 3^(5x+3+3x).

So, f(x) = 5x + 3 + 3x = 8x + 3.

Hence, the expression in terms of f(x) is:

3^f(x) = 3^(8x+3).