Question

Gente,
Quanto é 6^X = 10 ?

Answer 1

→ Lembrete:

⇒ $\log _b\left(a^c\right)=c\cdot \log _b\left(a\right)$
⇒ $\log _b\left(a\cdot c\right)=\log _b\left(a\right)+\log \:_b\left(c\right)$
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→ Adote:

⇒ $\log \left(2\right)\approx 0,3$
⇒ $\log \left(3\right)\approx 0,48$
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$6^x=10\\\log \left(6^x\right)=\log \:\left(10\right)\\x\cdot \log \left(6\right)=1\\x\cdot \log \left(2\cdot 3\right)=1\\x\cdot \left(\log \left(2\right)+\log \:\left(3\right)\right)=1\\x=\frac{1}{\log \:\left(2\right)+\log \:\:\left(3\right)}\\x\approx\frac{1}{0,3+0,48}\\x\approx\frac{1}{0,78}\\\boxed{\bold{x\approx 1,28}}$

Answer 2

6ˣ = 10

log6ˣ = log10

x.log6 = 1

x = 1/log6

x ≈ 1/0,778

x ≈ 1,285