The equation 8^x = 8x is not always true for all values of x. For some values of x, the left-hand side (LHS) will be larger than the right-hand side (RHS), and for some values, the RHS will be larger than the LHS.

For example, when x = 1, the LHS is 8 and the RHS is 8, so the equation is true for x = 1. However, for x = 2, the LHS is 64 and the RHS is 16, so the equation is not true for x = 2.

In general, there is no exact solution for x that satisfies the equation 8^x = 8x for all values of x.

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The equation 8^x = 8x can be solved for x using logarithmic properties. Taking the log base 8 of both sides:

log8(8^x) = log8(8x)

x = log8(8x)

Applying the logarithm rules:

x = log8(8x)
x/8 = log8(x)

Using change of base formula:

x/8 = logx/log8

Raising both sides to the power of 8:

x = (logx/log8)^8

Unfortunately, this equation cannot be solved analytically and numerical methods or graphical representation are needed to approximate x.