SOLUTION: Solve for: a){{{ (squareroot of 2 ^ (squareroot of x)) = (squareroot of 2^x) }}} b) {{{ 2 ^x^2 = (2^x)^2}}} c) {{{ 2 ^(x+3) = 2 ^x +3}}} d) {{{ log(3x) = 3 log x }}} Th

Question 120721: Solve for:
a)
b)
c)
d)

Thank you so much! :)
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
I'll do b, c, and d. Your rendering for part a is ambiguous. Do you mean or ?

b.)

Take the base-2 log of both sides:

Remembering that we can say:

and then apply the rule again to say:

Now remember that we can simplify to:

, or

c.

Remember that , so:

Add to both sides:

Factor out

Take the log base 2 of both sides:

Again, using we can say:

or if you prefer.

d.

Using in reverse we can say:

Take the antilog of both sides:

Only the positive square root will do because the domain of the function is constrained to
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