700=(4000)(0.65)z

Rewrite the equation as (4000)(0.65)z=700.

(4000)(0.65)z=700

Divide each term in (4000)(0.65)z=700 by 4000.

(4000)(0.65)z4000=7004000

Cancel the common factor of 4000.

Cancel the common factor.

4000(0.65)z4000=7004000

Divide (0.65)z by 1.

(0.65)z=7004000

0.65z=7004000

Cancel the common factor of 700 and 4000.

Factor 100 out of 700.

0.65z=100(7)4000

Cancel the common factors.

Factor 100 out of 4000.

0.65z=100⋅7100⋅40

Cancel the common factor.

0.65z=100⋅7100⋅40

Rewrite the expression.

0.65z=740

0.65z=740

0.65z=740

0.65z=740

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

ln(0.65z)=ln(740)

Expand ln(0.65z) by moving z outside the logarithm.

zln(0.65)=ln(740)

Divide each term in zln(0.65)=ln(740) by ln(0.65).

zln(0.65)ln(0.65)=ln(740)ln(0.65)

Cancel the common factor of ln(0.65).

Cancel the common factor.

zln(0.65)ln(0.65)=ln(740)ln(0.65)

Divide z by 1.

z=ln(740)ln(0.65)

z=ln(740)ln(0.65)

z=ln(740)ln(0.65)

The result can be shown in multiple forms.

Exact Form:

z=ln(740)ln(0.65)

Decimal Form:

z=4.04605020…

Solve for z 700=(4000)(0.65)^z