st3he1d0t

st3he1d0t

Answered

2022-09-04

Logarithm problem with two bases
Given
log x 9 + log 9 x = 10 3 .
How can I find the greatest value of x that satisfies the equation above?

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Recalculate according to your conditions!

Answer & Explanation

Salma Baird

Salma Baird

Expert

2022-09-05Added 8 answers

hint: a = log 9 x, then you have a quadratic in a:
a + 1 a = 10 3

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Bergsteinj0

Bergsteinj0

Expert

2022-09-06Added 1 answers

Let log x 9 = t ; 1 log x 9 = 1 t
Solve t + 1 t = 10 3
3 t 2 + 3 = 10 t
3 t 2 10 t + 3 = 0
t = 10 ± 100 4.3.3 6 = 3 or 1 3 .
So log x 9 = 3 or 1 3
Solve them, you will not get a neat answer, but an answer.

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