What is x ? 3^(x-3) = 17

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to find x for 3^(x-3) = 17

3^(x-3) = 17

take the logarithm of both the sides

log 3^(x-3) =  log 17

Now log x^a = a*log x

=> (x - 3)* log 3 = log 17

=> x - 3 = log 17 / log 3

=> x= 3 + log 17/ log 3

=> x = 5.5789

Therefore x = 5.5789

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

3^(x-3) = 17.

Let us apply the logarithm to both sides:

==> log 3^(x-3) = log 17.

Now from logarithm properties, we know that log a^b = b*log a

==> log 3^(x-3) = (x-3)*log 3.

==> (x-3)*log 3 = log 17.

Now we will divide by log 3.

==> x-3 = log 17/log 3

==>  x-3 = 2.58 ( approx.)

Now we will add 3 to both sides:

==> x = 3 + 2.58 = 5.58 ( approx.)

==> x = 5.58  OR   x = log17/log 3  + 3

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

To determine x, we'll take log on both sides:

log 3^(x-3)=log 17

We'll use the power rule of logarithms:

(x-3)*log 3 = log 17

We'll divide by log 3 both sides of the equation:

(x-3) = log 17 / log 3

We'll add 3  both sides:

x = log 17 / log 3 + 3

We'll compute the ratio log 17 / log 3 + 3:

log 17 / log 3 = 1.2304/0.4771 + 3

x = 2.6617/0.4771

x = 5.5789 approx.

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