3-log(x+2)=5
Looking at laws of log:
log(a+b)
3- log x + log 2 = 5
3- log x + .30103 = 5
Combining like terms, and moving log to the other side so we can stay positive
3- log x + .30103 = 5
+ log x -5
3+.30103-5 = log x
you can continue doing this and isolate x by using the antilog.
log(a+b) is NOT log a + log b
log(ab) = log a + log b
3-log(x+2)=5
log(x+2) = -2
assuming base 10,
x+2 = 1/100
x = 1/100 - 2 = -1.99
To find the value of x in the equation 3 - log(x + 2) = 5, we can follow these steps:
Step 1: Move the constant term to the other side of the equation to isolate the logarithmic term.
3 - log(x + 2) = 5
-log(x + 2) = 5 - 3
-log(x + 2) = 2
Step 2: To remove the negative sign, multiply both sides of the equation by -1.
-1 * (-log(x + 2)) = -1 * 2
log(x + 2) = -2
Step 3: Rewrite the logarithmic equation in exponential form.
log(x + 2) = -2 is equivalent to 10^(-2) = x + 2
Step 4: Solve for x.
10^(-2) = x + 2
Step 5: Subtract 2 from both sides of the equation.
10^(-2) - 2 = x
Step 6: Simplify the left side of the equation.
0.01 - 2 = x
Step 7: Evaluate the left side.
x = -1.99
Therefore, the solution to the equation 3 - log(x + 2) = 5 is x = -1.99.