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secondary 3 | A Maths
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Pls help with this qn
Pls reply asap thx.
Qn is to solve for x
Date Posted: 3 years ago
Views: 400
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6^(3x) - 3^(x²) = 0
(6³)^x = 3^(x²)
((2×3)³)^x = (3^x)^x
((2³×3³))^x = (3^x)^x
For this equation to hold, x = 0 (so both sides become = 1)
or
2³ × 3³ = 3^x
Taking log3 on both sides,
log3 (2³ × 3³) = log3 (3^x)
log3 (2³) + log3 (3³) = xlog3 (3)
3 log3 (2) + 3log3 (3) = x
3 ln2/ln3 + 3 = x
∴ x = 0 or x = 3ln2/ln3 + 3
Alternative working in comments section
(6³)^x = 3^(x²)
((2×3)³)^x = (3^x)^x
((2³×3³))^x = (3^x)^x
For this equation to hold, x = 0 (so both sides become = 1)
or
2³ × 3³ = 3^x
Taking log3 on both sides,
log3 (2³ × 3³) = log3 (3^x)
log3 (2³) + log3 (3³) = xlog3 (3)
3 log3 (2) + 3log3 (3) = x
3 ln2/ln3 + 3 = x
∴ x = 0 or x = 3ln2/ln3 + 3
Alternative working in comments section
6^(3x) - 3^(x²) = 0
6^(3x) = 3^(x²)
Taking ln on both sides,
ln 6^(3x) = ln 3^(x²)
3x ln 6 = x² ln3
3x ln (2×3) = x² ln 3
3x (ln 2 + ln 3) = x² ln 3
3x (ln 2 + ln 3) - x² ln 3 = 0
x(3ln 2 + 3ln 3 - x ln 3) = 0
x = 0 or
3 ln 2 + 3 ln 3 - x ln 3 = 0
3ln 2 + 3 ln 3 = x ln 3
3ln2/ln3 + 3 = x
So x = 0 or x = 3ln2/ln3 + 3
6^(3x) = 3^(x²)
Taking ln on both sides,
ln 6^(3x) = ln 3^(x²)
3x ln 6 = x² ln3
3x ln (2×3) = x² ln 3
3x (ln 2 + ln 3) = x² ln 3
3x (ln 2 + ln 3) - x² ln 3 = 0
x(3ln 2 + 3ln 3 - x ln 3) = 0
x = 0 or
3 ln 2 + 3 ln 3 - x ln 3 = 0
3ln 2 + 3 ln 3 = x ln 3
3ln2/ln3 + 3 = x
So x = 0 or x = 3ln2/ln3 + 3
Can write on a paper . Very confusing but thx
No access to pen and paper currently. If have later I'll post
Thanksss
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Method 1. Anything not sure just ask.
Date Posted:
3 years ago
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Method 2
Date Posted:
3 years ago
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