How would I solve this LOG problem (different bases) 10 points?

log(base 2)(2x+1) - log(base 4)x = log(base 2)3

Add: log(base 4)x; to both sides

subtract: log(base 2)3; to both sides

you're left with: log(base 2)(2x+1) - log(base 2)3= log(base 4)x

using properties of logarithms you take the left hand side of the equation and you divide both quotients like so:

log(base2)(2x+1/3).

Now, we want to get everything into base 2 so that we can simplify. Look at the right hand of the equation, you have base 4. 4 is equal to 2^2 or which is the same as log(base2^2)x.

We're left with this:

log(base2)(2x+1/3).=log(base2)2x

we simplify log(base2) on both sides and we have: (2x+1)/3=2x........2x+1=6x........1=4x......x=1/4.

Substitute x=1/4 into your original equation and you'll see it works out!

Good luck!

log(base 2)(2x + 1) - log(base 2)(√x) = log(base 2) 3

log(base 2)[(2x + 1)/(√x)] = log(base 2) 3

(2x + 1) = 3√x

Solve for x.