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tester [92]
3 years ago
6

What is the solution to the equation 9^(−3x) ≈ 7?

Mathematics
2 answers:
ASHA 777 [7]3 years ago
7 0

Answer:

x = −0.295

Step-by-step explanation:

Given : 9^{(-3x)} \sim 7

To Find : value of x

Solution:

9^{(-3x)} \sim 7

Taking log both sides

\log{9^{(-3x)} \sim \log 7

Using property: \log a^n= n \log a

So, (-3x)\log 9 \sim \log 7

x \sim \frac{\log 7}{-3 \log 9}

x \sim \frac{\log 7}{-3 \log 9}

x \sim -0.295

Thus Option c is correct.

Hence  x = −0.295

Paraphin [41]3 years ago
6 0

9^{-3x}=7\ \ \ \ |ln\\\\\ln9^{-3x}=\ln7\ \ \ \ |use\ \log a^n=n\log a\\\\-3x\ln9=\ln7\ \ \ \ |:(-3\ln9)\\\\x=\dfrac{\ln7}{-3\ln9}\to x\approx-\dfrac{1.9459}{3\cdot2.1972}\to x\approx-0.295\\\\Answer:\ c)\ x=-0.295

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