Question

solve 5^(3x-9)-10=-2
Give the exact solution and an approximate solution to three decimal places.
x = (blank) ≈ (blank)

Answer 1

Answer:

x = 3.431

Step-by-step explanation:

Given equation is,

$5^{(3x-9)}-10=-2$

$5^{3x-9}-10+10=-2+10$

$5^{3x-9}=8$

By taking log on both the sides of the equation,

$\text{log}(5^{3x-9})=\text{log}8$

(3x - 9)log5 = log8

3x - 9 = $\frac{\text{log}8}{\text{log}5}$

3x - 9 = 1.292

3x = 9 + 1.292

x = $\frac{10.29202}{3}$

x = 3.4306

x ≈ 3.431