ethan760
contestada

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

a) x = 0.376
b) x = 0.295
c) x = −0.295
d) x = −0.376

Respuesta :

gmany

[tex] 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 [/tex]

Answer:

x = −0.295

Step-by-step explanation:

Given : [tex]9^{(-3x)} \sim 7[/tex]

To Find : value of x

Solution:

[tex]9^{(-3x)} \sim 7[/tex]

Taking log both sides

[tex]\log{9^{(-3x)} \sim \log 7[/tex]

Using property: [tex]\log a^n= n \log a[/tex]

So, [tex](-3x)\log 9 \sim \log 7[/tex]

[tex]x \sim \frac{\log 7}{-3 \log 9}[/tex]

[tex]x \sim \frac{\log 7}{-3 \log 9}[/tex]

[tex]x \sim -0.295 [/tex]

Thus Option c is correct.

Hence  x = −0.295