Log3(1+log2(1+3log5x))=3

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вопрос

To solve the given equation, we start by simplifying the expression inside the logarithms.

Let y = log5x.

So, the equation becomes:

log3(1 + log2(1 + 3y)) = 3

Now, simplify the expression inside:

log2(1 + 3y) = 2^3
1 + 3y = 8
3y = 7
y = 7/3

Now, substitute back in the original expression for y:

log5x = 7/3

Rewrite in exponential form:

5^(7/3) = x

x = 5^(7/3)