Solve for z 1.667=(1+0.03)^z

Math
1.667=(1+0.03)z
Rewrite the equation as (1+0.03)z=1.667.
(1+0.03)z=1.667
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
ln((1+0.03)z)=ln(1.667)
Expand the left side.
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Expand ln((1+0.03)z) by moving z outside the logarithm.
zln(1+0.03)=ln(1.667)
Add 1 and 0.03.
zln(1.03)=ln(1.667)
zln(1.03)=ln(1.667)
Divide each term by ln(1.03) and simplify.
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Divide each term in zln(1.03)=ln(1.667) by ln(1.03).
zln(1.03)ln(1.03)=ln(1.667)ln(1.03)
Cancel the common factor of ln(1.03).
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Cancel the common factor.
zln(1.03)ln(1.03)=ln(1.667)ln(1.03)
Divide z by 1.
z=ln(1.667)ln(1.03)
z=ln(1.667)ln(1.03)
z=ln(1.667)ln(1.03)
The result can be shown in multiple forms.
Exact Form:
z=ln(1.667)ln(1.03)
Decimal Form:
z=17.28844083…
Solve for z 1.667=(1+0.03)^z

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