Ask Question
25 June, 12:54

If 3 to the power of x+1 = 81 and 81 to the power of x-y = 3 then what is the value of x and y?

+4
Answers (1)
  1. 25 June, 13:50
    0
    From 1st condition:

    3^ (x+1) = 81

    Take log on both sides,

    ➡ log [3^ (x+1) ]=log81

    Use the property: log (x^a) = a logx

    ➡ (x+1) log 3=log (3⁴)

    ➡ (x+1) log 3=4*log 3

    ➡ (x+1) = 4 (log 3 / log 3)

    ➡ x+1=4

    ➡ x=3➡↪➡↪ ANS

    From 2nd condition, (Same process are repeated)

    81^ (x-y) = 3

    ➡ 3^4 (x-y) = 3

    ➡ log [3^4 (3-y) ]=log 3

    ➡ 4 (3-y) log 3=log 3

    ➡ (3-y) = (log 3) / (4log 3)

    ➡ 3-y = (1/4)

    ➡ y=11/4 ➡↪➡↪ ANS
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “If 3 to the power of x+1 = 81 and 81 to the power of x-y = 3 then what is the value of x and y? ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers