(43)y=(2764)
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
ln((43)y)=ln(2764)
Expand ln((43)y) by moving y outside the logarithm.
yln(43)=ln(2764)
Rewrite ln(43) as ln(4)-ln(3).
y(ln(4)-ln(3))=ln(2764)
y(ln(4)-ln(3))=ln(2764)
Use the quotient property of logarithms, logb(x)-logb(y)=logb(xy).
yln(43)=ln(2764)
Divide each term in yln(43)=ln(2764) by ln(43).
yln(43)ln(43)=ln(2764)ln(43)
Cancel the common factor of ln(43).
Cancel the common factor.
yln(43)ln(43)=ln(2764)ln(43)
Divide y by 1.
y=ln(2764)ln(43)
y=ln(2764)ln(43)
y=ln(2764)ln(43)
The result can be shown in multiple forms.
Exact Form:
y=ln(2764)ln(43)
Decimal Form:
y=-3
Solve for y (4/3)^y=(27/64)
