Properties of logarithmic and converting equation?

Question

How would I convert an equation like -1/2logbaseb(x+3)+1 to ln form so that I can graph it on my calculator.

WOOPS, I meant to write -1/2logbase2(x+3)+1. Sorry.

Answer 1

I don't know about graphing calculators, but to convert a logarithm from base b to base e you use the formula:
log(base b)(x) = log(base e)(x) / log(base e)(b).

Thus, putting b = 2 in line with your correction:
- (1/2)log(base 2)(x+3)+1
= - log(base e)(x+3) / 2 log(base e)(2) + 1.

Answer 2

Is the problem just the base of the log?

log base 2 (x+3) can be rewritten as:
ln(x+3)/ln(2)

ln(2) is a constant that you can just plug in, it's about 0.69315.

Can your calculator do:

(-0.5) * ln(x+3) / (0.69315) + 1

You can combine the two constants -0.5 and 0.69315 as well:

(-0.5) * ln(x+3) / (0.69315) + 1
((-0.5) / (0.69315)) * ln(x+3) + 1
-0.72135 * ln(x+3) + 1