Question

1)log1x=-2 2)log7(x-1)=1

Answer 1

1) х=1⁻²=1

2) х-1=7¹
    х-1=7
     х=7+1=8

Answer 2

1. To solve the equation log₁ₐ(x) = b, we can rewrite it in exponential form as aᵇ = x. In this case, we have log₁ₓ(1) = -2. So we rewrite it as x⁻² = 1, which gives us x = ±1. However, since the logarithm is only defined for positive values of x, we must discard the negative solution. Therefore, the solution to the equation is x = 1.

2. To solve the equation log₇(x - 1) = 1, we can rewrite it in exponential form as 7¹ = x - 1. Solving for x, we get x = 8. However, we need to check if this solution satisfies the domain of the logarithmic function, which is x - 1 > 0, or x > 1. Since 8 > 1, the solution is valid. Therefore, the solution to the equation is x = 8.