MATH SOLVE

4 months ago

Q:
# solve the exponential equation125^8x-2=150

Accepted Solution

A:

I presume the question is 125^(8x - 2) = 150 ?

If so, lg (has a base of 10) both sides of the equation,

lg 125^(8x - 2) = lg 150

<Bring the power down to the left, using formulae of lg (a)^b = b × lg a>

=> (8x - 2) × lg 125 = lg 150

=> (8x - 2) × lg 5^3 = lg 150

=> 3(8x - 2) × lg 5 = lg 150

=> (24x - 6) × lg 5 = lg 150

=> 24x - 6 = lg 150 ÷ lg 5

=> 24x = (lg 150 ÷ lg 5) + 6

=> x = [(lg 150 ÷ lg 5) + 6] ÷ 24

=> x ~ 0.379 (rounded off to 3 significant factors)

Hope this helps! :)

If so, lg (has a base of 10) both sides of the equation,

lg 125^(8x - 2) = lg 150

<Bring the power down to the left, using formulae of lg (a)^b = b × lg a>

=> (8x - 2) × lg 125 = lg 150

=> (8x - 2) × lg 5^3 = lg 150

=> 3(8x - 2) × lg 5 = lg 150

=> (24x - 6) × lg 5 = lg 150

=> 24x - 6 = lg 150 ÷ lg 5

=> 24x = (lg 150 ÷ lg 5) + 6

=> x = [(lg 150 ÷ lg 5) + 6] ÷ 24

=> x ~ 0.379 (rounded off to 3 significant factors)

Hope this helps! :)