^{x-3}=(2/3)

_{10}) of both sides and you get:

^{x-3}=ln(2/3)

^{x}=xln(A) we get:

Solve the exponential equation.

x - 3

{ 1 } = 2

6 3

(type a integer or a decimal. Round to the nearest thousandth as needed. Use a comma to seperate the answers as needed)

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Charles A. | Math major at Old Dominion for math tutoringMath major at Old Dominion for math tuto...

TO solve this equation we use logarithms as follows:

(1/6)^{x-3}=(2/3)

Take the natural logarithm (can also use log_{10}) of both sides and you get:

ln(1/6)^{x-3}=ln(2/3)

Because of the logarithmic property: ln(A)^{x}=xln(A) we get:

(x-3)ln(1/6)=ln(2/3)

If we divide both sides by ln(1/6) we get:

x-3=[ln(2/3)]/[ln(1/6)]

add 3 to both sides and we get:

x=[ln(2/3)]/[ln(1/6)]+3

which has a decimal expansion as follows:

3.226 (rounded to thousandth as requested)

Hope this helps :)

(1/6)^(x-3) = 2/3

log((1/6)^(x-3)) = log(2/3)

(x-3) log(1/6) = log(2/3)

x log(1/6) - 3 log(1/6) = log(2/3)

x log(1/6) = 3 log(1/6) + log(2/3)

x = 3 + log(2/3)/log(1/6)

x ≈ 3.22629438553092 ≈ 3.226

check:

(1/6)^(3.22629438553092-3) =? 2/3

0.666666666666666 = 2/3 √

Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...

(1/6) ^( X -3) = 2/3

( X -3 ) log ( 1/6) = log( 2/3)

X -3 = log ( 2/3) / log ( 1/6)

X = 3 + 0.2263 = 3. 2263

Test :

( 1/6) ^ ( 0.2263) = 0.66665996

It works.

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