Find value of $$ X $$ $$ x^{X}=256 $$

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UpStudy AI · Accepted Answer

The equation is given by

x^X = 256.

To solve for X in terms of x, we can use logarithms. Assuming x > 0 (with x ≠ 1), we take the natural logarithm of both sides:

ln(x^X) = ln(256).

Using the logarithmic identity ln(a^b) = b · ln(a), we have:

X · ln(x) = ln(256).

Now, solve for X:

X = ln(256) / ln(x).

Thus, the solution is

X = (ln 256) / (ln x).

Note that since 256 = 2^8, different choices for x will give specific numerical values for X. For example:
 • If x = 2, then X = ln(256)/ln(2) = 8.
 • If x = 4, then X = ln(256)/ln(4) = 4.
 • If x = 16, then X = ln(256)/ln(16) = 2.

Without additional information about x, the most general answer is X = (ln 256)/(ln x).
To find the value of $$ X $$ in the equation $$ x^{X} = 256 $$, take the natural logarithm of both sides: $$ X = \frac{\ln(256)}{\ln(x)} $$ This gives the general solution for $$ X $$ in terms of $$ x $$.

Find value of \( X \) \( x^{X}=256 \)

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