Question

Log3(x^2-48)=log3(1)

Answer 1

Log3(x^2-48)=log3(1)
x^2-48=1
x^2-49=0
(x-7)(x+7)=0
x=7
x=-7

Answer 2

The equation you provided is:

log₃(x² - 48) = log₃(1)

In logarithmic equations, if both sides have the same base, and the logarithms are equal, then the arguments (the expressions within the logarithms) must also be equal. Therefore, we can set the arguments equal to each other:

x² - 48 = 1

Now, let's solve this equation for x.

x² - 48 = 1

Adding 48 to both sides:

x² = 49

Taking the square root of both sides:

x = ±√49

x = ±7

Therefore, the solutions to the equation log₃(x² - 48) = log₃(1) are x = 7 and x = -7.