Question

Solve
Xlog4 base 10=log8 base 10 + logX base 10

Answer 1

To solve the equation Xlog4 base 10 = log8 base 10 + logX base 10, we can use the properties of logarithms.

First, we can simplify the logarithmic expressions using the property loga + logb = logab.

Xlog4 base 10 = log8 base 10 + logX base 10
Xlog4 base 10 = log(8X) base 10

Next, we can convert the equation to exponential form. In exponential form, the base is raised to the power of the logarithm to obtain the value.

10^(Xlog4 base 10) = 10^(log(8X) base 10)

Using the property loga(x) = y is equivalent to saying a^y = x, we can rewrite the equation as:

4^X = 8X

To further solve the equation, we can try different values of X and see if they satisfy the equation.

For X = 2, we have:
4^2 = 8(2)
16 = 16

For X = 3, we have:
4^3 = 8(3)
64 = 24

Therefore, X = 2 is the solution to the equation.