Given the equation below, what is the value of x? 3^(x)=21?

3^x=21
=>
xln(3)=ln(21)
=>
x=ln(21)/ln(3)=?
Use your calculator to find the answer.

3^x = 21
xln(3) = ln(21)

x = ln(21)/ln(3)
x = 2.7712

3^x = 21
ln(3^x) = ln21
x * ln3 = ln21
x = ln21/ln3

3^x = 21

If we get the log of both sides we get:

ln(3^x) = ln(21)

We can now move the exponent out of the log:

x ln(3) = ln(21)

Divide both sides by ln(3):

x = ln(21) / ln(3)

That's your exact answer.  If you want a decimal approximation rounded to a few digits a calculator gives us:

x = 2.771244 (rounded to 6DP)

log3(3^x) = log3(21)
x = log3(21) = log(21)/log(3) = 1.32/0.477 = 2.77

Verify

3^2.77 = 21