Solve the equation below. Please show all of your work

log_7(x + 3/7) = -2

7^ [log_7(x + 3/7)]

= x + 3/7 = 7^-2 = -1/49

x + 3/7 = -1/49
x = -21/49 - 1/49 = -22/49

You make it look so easy and I have been pounding my head on the wall. Thank you!

except for the sign error

7^ [log_7(x + 3/7)]
= x + 3/7 = 7^-2 = 1/49

x + 3/7 = 1/49
x = -21/49 + 1/49 = -20/49

To solve the equation log_7(x + 3/7) = -2, you need to eliminate the logarithm by raising both sides of the equation to the exponent of the base 7.

Step 1: Raise both sides to the exponent of 7:

7^(log_7(x + 3/7)) = 7^(-2)

Step 2: Simplify the left side using the logarithm property:

x + 3/7 = 7^(-2)

Step 3: Simplify the right side:

x + 3/7 = 1/7^2 = 1/49

Step 4: Subtract 3/7 from both sides to isolate x:

x = 1/49 - 3/7

Step 5: Find a common denominator to subtract the fractions:

x = 1/49 - (3/7) * (7/7)
x = 1/49 - 21/49
x = (1 - 21)/49
x = -20/49

So, the solution to the equation log_7(x + 3/7) = -2 is x = -20/49.