Answer the following:

Question

asked Jun 24, 2024 23.4k views

1 Answer

Adedoyin Akande · Answer 1 · 2024-06-29T16:05:28+0000

Answer:

x = 2

Explanation:

First, we can rewrite all of the constants as exponential representations of 5.

$(5^(3x)\cdot 5^2)/(5^x) = 5^3\cdot 5^3$

(5^(3x + 2))/(5^x) = 5^(3 + 3)

(5^(3x + 2))/(5^x) = 5^6

Next, we can take the log base 5 of both sides.

$\log_5\left((5^(3x + 2))/(5^x)\right) = \log_5(5^6)$

$\log_5\left((5^(3x + 2))/(5^x)\right) = 6$

Then, we can apply the log quotient rule to the left side:

$\log\left((x)/(y)\right) = \log(x) - \log(y)$

$\log_5(5^(3x + 2)}) - \log_5(5^x) = 6$

(3x + 2) - x = 6

Finally, we can solve by combining like terms, then isolating x.

2x + 2 = 6

2x = 4

$\boxed{x=2}$