Log5(x+12)=log9(x+12)

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вопрос

To solve this equation, we can first convert both sides to exponential form using the property of logarithms:

For the left side of the equation
log5(x+12) = y can be rewritten as 5^y = x + 12

For the right side of the equation
log9(x+12) = z can be rewritten as 9^z = x + 12

Now, we have
5^y = x + 1
9^z = x + 12

Since x + 12 is the same on both sides, we can set the two exponential equations equal to each other:

5^y = 9^z

To make the bases the same, we can rewrite 9 as 3^2:

5^y = (3^2)^
5^y = 3^(2z)

Now, we can see that 5 is not a power of 3 and vice versa, so we cannot easily simplify this further.

Therefore, the equation log5(x+12) = log9(x+12) does not simplify to a single value and cannot be solved as is. It is not possible to determine a unique solution for x based on the information given in the original equation.