Final answer:
The solution to the equation 4^(3x-1)=32^(x+5) is found by utilizing logarithmic properties to rewrite the equation in a simpler form. The final result is x = 27.
Step-by-step explanation:
To find the solution to the equation 4^(3x-1)=32^(x+5), we need to use logarithmic properties. Firstly, remember that 32 can be rewritten as 2^5 and 4 as 2^2, making our equation 2^(6x-2) = 2^5^(x+5).
Using the property of logarithms, if the bases are equal we can set the exponents equal to each other. So, we get 6x - 2 = 5x + 25. Solving for x, we subtract 5x from both sides, resulting in: x - 2 = 25. Adding 2 to both sides gives us the main answer: x = 27.
In conclusion, applying logarithmic properties allowed us to simplify and solve for x in the given equation.
Learn more about logarithmic properties