Question

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

Answer 1

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

Answer 2

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