log(a)log(6)=y

Multiply both sides of the equation by log(6).

log(6)⋅log(a)log(6)=log(6)⋅y

Cancel the common factor of log(6).

Cancel the common factor.

log(6)⋅log(a)log(6)=log(6)⋅y

Rewrite the expression.

log(a)=log(6)⋅y

log(a)=log(6)⋅y

Reorder factors in log(6)y.

log(a)=ylog(6)

log(a)=ylog(6)

Rewrite log(a)=ylog(6) in exponential form using the definition of a logarithm. If x and b are positive real numbers and b≠1, then logb(x)=y is equivalent to by=x.

10ylog(6)=a

Rewrite log(6) as log(2(3)).

10ylog(2(3))=a

Rewrite log(2(3)) as log(2)+log(3).

10y(log(2)+log(3))=a

Apply the distributive property.

10ylog(2)+ylog(3)=a

Rewrite the equation as a=10ylog(2)+ylog(3).

a=10ylog(2)+ylog(3)

a=10ylog(2)+ylog(3)

Solve for a ( log of a)/( log of 6)=y