need some help with these questions PLEASE
1.
solve the equation
0.5 ^(1+3x)=7
giging you answer to 2 decimal places
2.
log (5x) - log(1/x+1)=2log(2x+2)
to #1:
$\displaystyle \left(\dfrac12\right)^{1+3x} = 7~\iff~\dfrac12 \left(\dfrac18\right)^x=7~\implies~$ $\displaystyle \left(\dfrac18\right)^x=14~\implies~8^x=\dfrac1{14 }~\implies~x=\log_8\left(\dfrac1{14}\right)~\impli es~$ $\displaystyle x=\log_8\left(14^{-1}\right)~\implies~x=\dfrac{-\ln(14)}{\ln(8)}$
to #2:
Unfortunately the writing isn't clear. I assume that you mean:
$\displaystyle \log(5x)-\log\left(\dfrac1{x+1}\right)=2\log(2x+2)~\implies ~\log(5x(x+1))=\log((2x+2)^2)$
Solve for x:
$\displaystyle 5x(x+1)=(2x+2)^2~\iff~5x(x+1)=4(x+1)^2~\implies~x=-1~\vee~x=4$
Keep in mind that the log-function is defined for positive values only and therefore x = -1 is not a solution of this equation!
EDIT: Removed a mistake
Remember that ....$\displaystyle 0.5=\dfrac12$
So I've done your question in my previous post. I didn't give you the approximative number because I was pretty sure that you can calculate it yourself. For confirmation $\displaystyle x\approx -1.27$
EDIT: I've corrected my previous post. Have a look!