SOMEONE PLEASE HELP ME WITH THIS MATH PROBLEM!!!!!!!!!!!!!!!!

Solving a logarithmic equation.
Solve each equation. Check your answers.

2 log x = -1

2 log ( x + 1 ) = 5


please explain!!!

2 logx = -1 <=> logx = -1/2 <=> x = 10^-1/2 <=> x = sqrt(10)/10

2 log(x+1) = 5 <=> log(x+1)=5/2 <=> x+1 = 10^(5/2) <=> x = 100sqrt(10) + 1

You should remember that, logx = y <=> x = 10^y
This is for logarithms that have number 10 as a base. Generally log(a)x = y <=> x = a^y

What I do with this sort of problem is recall these facts

log 100 = 2
so
10^2 = 100

log 1000 = 3
so
10^3 = 1000
Remember that log means log to the base 10 and ln means log to base e.


So, we have

2 log x = - 1

log x = - 1/2 = - 0.5

x = 10 ^ (-0.5) = 1 / 10^0.5 = 1 / √10 = 0.316

For the the second one, we have

2 log (x + 1) = 5

log (x + 1) = 5/2 = 2.5

(x + 1) = 10^(2.5) = 316.23

x = 316.23 - 1 = 315.23

2log x = -1
So log x = -1/2
But notice that the log function is gives the number required for the base to be raised in power to give the number 'logarithmised'. So x is 10^(-1/2), which is 1/sqrt(10).

2log x+1 = 5
So log x+1 = 5/2
so x+1 = 10^(5/2) = 100sqrt(10). so x is 100sqrt(10) - 1.