Solve for x over the integers:
7^(x+2) = 7^(2 x+2)
Take logarithms of both sides to turn products into sums and powers into products.
Take the natural logarithm of both sides and use the identity log(a^b) = b log(a):
log(7) (x+2) = log(7) (2 x+2)
Write the linear polynomial on the left hand side in standard form.
Expand out terms of the left hand side:
log(7) x+2 log(7) = log(7) (2 x+2)
Write the linear polynomial on the right hand side in standard form.
Expand out terms of the right hand side:
log(7) x+2 log(7) = 2 log(7) x+2 log(7)
Isolate x to the left hand side.
Subtract 2 x log(7)+2 log(7) from both sides:
-(log(7) x) = 0
Divide both sides by a constant to simplify the equation.
Divide both sides by -log(7):
Answer:
x = 0
