solve the logarithmic equation.
log(5x+7)=1+log(x-9)
To solve the logarithmic equation log(5x+7) = 1 + log(x-9), we need to isolate the logarithmic term on one side of the equation and simplify it.
Step 1: Use the properties of logarithms to combine the terms on the right side of the equation.
log(5x+7) = log(10 * (x-9))
log(5x+7) = log(10x - 90)
Step 2: Now, we can equate the arguments of the logarithms, since the bases are the same.
5x + 7 = 10x - 90
Step 3: Simplify the equation by bringing similar terms together.
5x - 10x = -90 - 7
-5x = -97
Step 4: Divide both sides of the equation by -5 to solve for x.
x = -97 / -5
Step 5: Simplify the result.
x = 19.4
Therefore, the solution to the logarithmic equation log(5x+7) = 1 + log(x-9) is x = 19.4.