Question

What is the value of x that satisfies the equation?

27^(3x)=81^(x+10)

Answer 1

x=7.999996

Explanation:

273x=81x+10

log(273x)=log(81x+10)(Take log of both sides)

3x*(log(27))=(x+10)*(log(81))

3x=(

log(81)

log(27)

)*(x+10)

3x=1.333333*(x+10)

3x=1.333333x+13.33333(Simplify both sides of the equation)

3x−1.333333x=1.333333x+13.33333−1.333333x(Subtract 1.333333x from both sides)

1.666667x=13.33333

1.666667x

1.666667

=

13.33333

1.666667

(Divide both sides by 1.666667)