Question

5-39. solve each equation.

a. $\frac{2x - 8}{10} = 6$

b. $9^x = 3^{40}$

Explanation:

Step1: Eliminate denominator (part a)

Multiply both sides by 10:
$2x - 8 = 6 \times 10$
$2x - 8 = 60$

Step2: Isolate variable term (part a)

Add 8 to both sides:
$2x = 60 + 8$
$2x = 68$

Step3: Solve for x (part a)

Divide by 2:
$x = \frac{68}{2}$
$x = 34$

Step4: Rewrite base (part b)

Express 9 as $3^2$:
$(3^2)^x = 3^{40}$

Step5: Simplify exponent (part b)

Use exponent rule $(a^m)^n=a^{mn}$:
$3^{2x} = 3^{40}$

Step6: Equate exponents (part b)

Set exponents equal (same base):
$2x = 40$

Step7: Solve for x (part b)

Divide by 2:
$x = \frac{40}{2}$
$x = 20$

Answer:

a. $x = 34$
b. $x = 20$