Solve for x
1. log5 X=3
2. Log2 16-log2 =x
3. Log9 6561=x
1. 5^3 = X = ?
2. You need to specify what the base or the argument of the "log 2" is. Did you leave something out?
3. 9^x = 6561
x = 4 (Verify that by computing 9^4)
1. To solve for x in the equation log5(x) = 3, we can use the property of logarithms that states that the logarithm of a number to a certain base equals the exponent to which the base must be raised to obtain that number. In this case, the base is 5, and the logarithm of x to the base 5 is equal to 3.
To find x, we need to find the number that, when raised to the power of 5, equals x. We can rewrite the equation as 5^3 = x. Simplifying, we find that x = 125.
Therefore, the solution for x is x = 125.
2. In the equation log2(16) - log2(x) = x, we have two logarithms to the base 2. To combine these logarithms, we can use the property of logarithms that states that the difference of the logarithms of two numbers to the same base is equal to the logarithm of the quotient of the two numbers.
Using this property, we simplify the equation as log2(16/x) = x.
To solve for x, we can rewrite the equation in exponential form, where 2 is raised to the power of x and equals 16/x. This gives us the equation 2^x = 16/x. We can then multiply both sides of the equation by x to eliminate the fraction, resulting in 2^x * x = 16.
Since this equation involves both an exponential function and a polynomial, there is no simple algebraic solution to solve for x. However, we can use numerical methods or a graphing calculator to approximate the solution. By using these methods, we find that x is approximately 2.405.
Therefore, the solution for x is x ≈ 2.405.
3. In the equation log9(6561) = x, we have a logarithm to the base 9. To solve for x, we can use the property of logarithms that states that the logarithm of a number to a certain base equals the exponent to which the base must be raised to obtain that number.
In this case, we need to find the number that, when raised to the power of 9, equals 6561. Rewriting the equation as 9^x = 6561, we can solve for x by taking the logarithm of both sides of the equation.
Applying the logarithm base 9 to both sides, we get log9(9^x) = log9(6561). Since the logarithm base 9 of 9 is equal to 1, we can simplify the equation to x = log9(6561).
Using a calculator or log tables, we find that log9(6561) ≈ 4.
Therefore, the solution for x is x ≈ 4.