Question

Решите уравнение: log3(1+x)=3

Answer 1

$1 + x= 3 {}^{3}$
$x = 27 - 1$
$x = 26$
Ответ:26

Answer 2

To solve the equation log₃(1+x) = 3, we need to eliminate the logarithm and find the value of x. The equation can be rewritten in exponential form as follows:

3^log₃(1+x) = 3^3

Since logₓ(y) = z is equivalent to x^z = y, we have:

3^(log₃(1+x)) = 3^3

Now, by the property of logarithms, the base (3 in this case) and the exponent (log₃(1+x)) cancel each other out, leaving us with:

1 + x = 3^3

Simplifying the right-hand side:

1 + x = 27

Now, isolate x:

x = 27 - 1

x = 26

So the solution to the equation is x = 26.