Final answer:
To solve the equation 2(5)ⁿ-4 = 246 using the like-bases property and exponents, we need to make sure the bases of the exponents are the same. By converting 5 to 5¹, we can apply the property of exponents and simplify the equation. The value of n is 3.
Step-by-step explanation:
The given equation is 2(5)ⁿ-4 = 246. To solve this equation using the like-bases property and exponents, we need to make sure the bases of the exponents are the same. In this case, the base is 5. We can rewrite 5 as 5¹, so the equation becomes 2(5¹)ⁿ-4 = 246.
Applying the property of exponents, we can multiply the exponents of 5 and 5¹, which results in 2(5ⁿ)⁻⁴ = 246.
Next, we simplify the equation by combining like terms and isolating the variable. We subtract 4 from the exponent, so the equation becomes 2(5ⁿ) = 250. Finally, we divide both sides of the equation by 2 to solve for the variable, which gives us 5ⁿ = 125. Therefore, the value of n is 3, because 5 raised to the power of 3 is equal to 125.