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

Math
700=(4000)(0.65)z
Rewrite the equation as (4000)(0.65)z=700.
(4000)(0.65)z=700
Divide each term by 4000 and simplify.
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Divide each term in (4000)(0.65)z=700 by 4000.
(4000)(0.65)z4000=7004000
Cancel the common factor of 4000.
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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.
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Factor 100 out of 700.
0.65z=100(7)4000
Cancel the common factors.
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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 by ln(0.65) and simplify.
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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).
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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

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