NEED HELP WITH EXPONENTIAL AND LOGARITHMIC FUNCTIONS

log(2x+3)=3 help me understand??

Question

NEED HELP WITH EXPONENTIAL AND LOGARITHMIC FUNCTIONS


log(2x+3)=3  help me understand??

anonymous · Answer

you are supposed to solve for $x$ right?

anonymous · Answer

yes i believe so.

anonymous · Answer

assuming this is log base ten, then 
$$\log(x)=y\iff 10^y=x$$

anonymous · Answer

why would we assume it is 10?? do we always do that?

anonymous · Answer

they are just different ways of saying the same thing
so if 
$$\log(2x+3)=3$$ that means 
$$2x+3=10^3$$ and you can solve for $x$

anonymous · Answer

ya give me a secccc

anonymous · Answer

if you don't see a base written, like $\log(x)$ instead of $\log_2(x)$ then you assume it is log base ten

anonymous · Answer

x=498.5?

anonymous · Answer

i guess

anonymous · Answer

$$2x+3=1000\
2x=997\
x=997\div 2$$ whatever that is

anonymous · Answer

yea thats exatly what my work looks like!!

anonymous · Answer

one of the answer choices is 997/2 so im guessing they dont want us to simplify??

anonymous · Answer

k
that was the routine part
the main part was to be able to go from logarithmic to exponential form quickly which is what you will need 
$$\large b^y=x\iff \log_b(x)=y$$

anonymous · Answer

yeah  i would go with $\frac{997}{2}$

anonymous · Answer

awesome! You are definitely going to go far in life! You are so smart and helpful!! thank you so much :)

anonymous · Answer

lol
thanks 
and your welcome