If 8^x=2 and 3^(x+y)=81 then y=?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We need to find y using 8^x=2 and 3^(x+y)=81.

First we find x using 8^x=2.

8^x=2

=> (2^3)^x = 2^1

=> 2^3x = 2^1

as the base is the same, we can equate the exponent. Therefore 3x = 1 or x = 1/3.

Now we substitute this in 3^(x+y)=81

=> 3^(1/3 + y) = 3^ 4

Again as the base is same equate the exponent.

=> 1/3 + y = 4

=> y = 4 - 1/3

=> y = 11/3

Therefore x = 1/3 and y = 11/3.

Top Answer

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll write 8^x = 2^3x

We'll re-write 8^x = 2 <=> 2^3x = 2

Since the bases are matching, we'll get:

3x = 1

We'll divide by 3:

x = 1/3

We'll use the product property of exponentials:

 3^(x+y)=3^x*3^y

We'll substitute x by 1/3 and we'll write 81 as a power of 3:

 3^(1/3 + y) = 3^4

Since the bases are matching, we'll get:

1/3 + y = 4

We'll subtract 1/3, to isolate y to the left side:

y = 4 - 1/3

y = 11/3

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