Question

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

Answer 1

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

Answer 2

x = −0.295

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 (\log 7)/(-3 \log 9)`

`x \sim (\log 7)/(-3 \log 9)`

`x \sim -0.295`

Thus Option c is correct.

Hence x = −0.295