log little 2 (3x^2) - log little two 6 =5
log2 (3x^2) - log2 6 =5
log2(3x^2/6) = 5
3x^2/6 = 2^5
3x^2 = 6*32
x^2 = 64
x = ± 8
online, many write log_2(3x^2) or log2(3x^2) to specify base 2,
if you don't know how to use the and tags.
To solve this logarithmic equation, we will apply the properties of logarithms.
First, we can simplify the equation using the quotient property of logarithms, which states that the logarithm of a quotient is equal to the difference of the logarithms of the numerator and denominator:
log2(3x^2/6) = 5
Next, we can simplify the numerator by canceling out the common factors. In this case, the common factor is 3:
log2(x^2/2) = 5
Now, we can use another property of logarithms, known as the power property, which states that the logarithm of a base raised to an exponent is equal to the product of the exponent and the logarithm of the base:
2^(log2(x^2/2)) = 2^5
Since the base of the logarithm and the base raised to an exponent are the same, we can cancel them out, resulting in:
x^2/2 = 32
To eliminate the division by 2, we can multiply both sides of the equation by 2:
2 * (x^2/2) = 2 * 32
x^2 = 64
Now, we can take the square root of both sides to solve for x:
√(x^2) = √64
x = ±8
Therefore, the equation has two solutions: x = 8 and x = -8.