Final answer:
To solve the equation log₃(4x)+log₃(6)=5 and find the value of x, we can use properties of logarithms. By simplifying and converting to exponential form, we can solve for x and round to the nearest hundredth.
Step-by-step explanation:
To solve the given equation log₃(4x)+log₃(6)=5 for x, we can use the properties of logarithms. the sum of logarithms with the same base is equal to the logarithm of their product. therefore, we can rewrite the equation as log₃(4x * 6) = 5.
Simplifying the expression inside the logarithm, we get log₃(24x) = 5. to remove the logarithm, we can convert it to exponential form, which gives us 3^5 = 24x.
Calculating 3^5, we find that 24x = 243. Finally, divide both sides by 24 to get the value of x, which is approximately 10.125 rounded to the nearest hundredth.