(2^(x))(5)=10^(x)
steps too please
how to solve
To solve the equation (2^(x))(5) = 10^(x), you can follow these steps:
Step 1: Simplify both sides of the equation:
On the left side, you can simplify (2^(x))(5) to 5 * 2^(x).
On the right side, 10^(x) remains the same.
The equation now becomes:
5 * 2^(x) = 10^(x)
Step 2: Rewrite the bases with the same base:
Since 5 is a factor of 10, we can rewrite 10^(x) as (5 * 2)^(x).
The equation now becomes:
5 * 2^(x) = (5 * 2)^(x)
Step 3: Apply the exponent properties:
Using the property (a * b)^(x) = a^(x) * b^(x), we can separate the exponents:
5 * 2^(x) = 5^(x) * 2^(x)
Step 4: Cancel the common term (2^(x)):
Since 2^(x) exists on both sides of the equation, we can divide both sides by 2^(x) to cancel it out:
5 = 5^(x)
Step 5: Solve for x:
Since the bases on both sides of the equation are the same, we can equate the exponents:
x = 1
So the solution to the equation (2^(x))(5) = 10^(x) is x = 1.