Solve the equation. Round answers to the nearest hundredth.

log(7x+1)=log(x-2)+1

one way:

log(7x+1)=log(x-2)+log(10)
7x+1 = (x-2)(10) = 10x-20
3x = 21
x = 7

other way:

log(7x+1)-log(x-2) = 1
log ((7x+1)/(x-2) = 1
(7x+1)/(x-2) = 10
7x+1 = 10(x-2)
. . .

Check:
log50 = log5 + log10

x/(x^(2)-4)+5x/(x^(2)-7x+10)

To solve the equation log(7x+1) = log(x-2) + 1, we need to eliminate the logarithms first.

Remember that the logarithm function is only defined for positive numbers, so we need to make sure that both (7x+1) and (x-2) are positive.

Since the logarithms on both sides of the equation have the same base (which is not specified), we can remove the logarithms by using exponential functions.

Here's how you can solve the equation step by step:

Step 1: Rewrite the equation using exponential functions:
10^(log(7x+1)) = 10^(log(x-2) + 1)

Step 2: Apply the power rule of logarithms:
7x + 1 = 10^(log(x-2)) * 10^1
7x + 1 = 10 * (x - 2)

Step 3: Distribute and simplify:
7x + 1 = 10x - 20

Step 4: Simplify further:
-3x = -21

Step 5: Solve for x:
x = (-21)/(-3)
x = 7

Therefore, the solution to the equation log(7x+1) = log(x-2) + 1 is x = 7.