Question

3Log(2024)(x)=7√x×163

Answer 1

To solve the equation, we can start by simplifying both sides.

First, let's simplify the right side of the equation:

7√x * 163 = 7 * √x * 163 = 7 * 163 * √x = 1141√x

Now, the equation becomes:

3Log(2024)(x) = 1141√x

To simplify further, we need to express both sides in terms of the same base.

Using the logarithmic property, we can convert the left side to base 10 logarithm:

3Log(2024)(x) = Log(10)(x) / Log(10)(2024)

Now, the equation becomes:

Log(10)(x) / Log(10)(2024) = 1141√x

To simplify further, let's eliminate the square root (√) by raising both sides of the equation to the power of 2:

[Log(10)(x) / Log(10)(2024)]^2 = (1141√x)^2

[Log(10)(x)]^2 / [Log(10)(2024)]^2 = 1141^2 * (√x)^2

[Log(10)(x)]^2 / [Log(10)(2024)]^2 = 1141^2 * x

Now, let's take the square root of both sides:

( Log(10)(x) / Log(10)(2024) ) = ± √( 1141^2 * x )

Log(10)(x) = ± √( 1141^2 * x ) * Log(10)(2024)

To solve for x, we need to isolate it. Let's start by eliminating the logarithm on the left side:

x = 10^[ ± √( 1141^2 * x ) * Log(10)(2024) ]

Now, this equation cannot be easily solved algebraically. We can use numerical methods such as approximation or iteration to find the value of x.