4^(1+2x)=64

Question

What does x equal?

Answer 1

There are two ways to do this. One involves using logarithms, but my guess is you haven't gotten there yet.

Look at your base 4. Let's look at 64. 64=4*4*4=4^3. Because of that we can rewrite 64 as 4^3 so both sides of the equation have the same base.

4^(1+2x)=4^3. Since the bases are the same, the exponents have to be the same. We can then set 1+2x =3. Solve our linear equation. 2x =2 x=1

Answer 2

Remember the formula.

y=b^x is equivalent to logb(y)=x

Put you equation in log form

log4(64)=1+2x

solve log4(64) by putting log(64)/log(4) into your calculator

3=1+2x

subtract 1 from both sides

2=2x

Divide both sides by 2

x=1