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) = 2^31 + 3y = 83y = 7y = 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)
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)