To solve the given equation, we need to simplify both sides by using the properties of logarithms. We can start by using the power rule of logarithms which states that log(a^n) = n log(a).
1) Simplify the left side of the equation: Log3x = 4 3x = 3^4 3x = 81 x = 27
2) Simplify the right side of the equation: Log56(3x-5) = Log56(2x) Since the bases of the logarithms are the same, we can drop the logarithms: 3x - 5 = 2x 3x - 2x = 5 x = 5
Therefore, the value of x that satisfies the equation is x = 5.
To solve the given equation, we need to simplify both sides by using the properties of logarithms. We can start by using the power rule of logarithms which states that log(a^n) = n log(a).
1) Simplify the left side of the equation:
Log3x = 4
3x = 3^4
3x = 81
x = 27
2) Simplify the right side of the equation:
Log56(3x-5) = Log56(2x)
Since the bases of the logarithms are the same, we can drop the logarithms:
3x - 5 = 2x
3x - 2x = 5
x = 5
Therefore, the value of x that satisfies the equation is x = 5.