Whakaoti i te 5000/x=1.08^10-1/0.08

$$\frac { 5000 } { x } = \frac { 1.08 ^ { 10 } - 1 } { 0.08 }$$

Whakaoti mō x

$$x = \frac{4768371582031250}{13815462556753} = 345\frac{2036999951465}{13815462556753} \approx 345.147443485$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x.

$$5000=x\times \frac{1.08^{10}-1}{0.08}$$

Tātaihia te 1.08 mā te pū o 10, kia riro ko 2.15892499727278669824.

$$5000=x\times \frac{2.15892499727278669824-1}{0.08}$$

Tangohia te 1 i te 2.15892499727278669824, ka 1.15892499727278669824.

$$5000=x\times \frac{1.15892499727278669824}{0.08}$$

Whakarohaina te \frac{1.15892499727278669824}{0.08} mā te whakarea i te taurunga me te tauraro ki te 100000000000000000000.

$$5000=x\times \frac{115892499727278669824}{8000000000000000000}$$

Whakahekea te hautanga \frac{115892499727278669824}{8000000000000000000} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2097152.

$$5000=x\times \frac{55261850227012}{3814697265625}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$x\times \frac{55261850227012}{3814697265625}=5000$$

Me whakarea ngā taha e rua ki te \frac{3814697265625}{55261850227012}, te tau utu o \frac{55261850227012}{3814697265625}.

$$x=5000\times \frac{3814697265625}{55261850227012}$$

Tuhia te 5000\times \frac{3814697265625}{55261850227012} hei hautanga kotahi.

$$x=\frac{5000\times 3814697265625}{55261850227012}$$

Whakareatia te 5000 ki te 3814697265625, ka 19073486328125000.

$$x=\frac{19073486328125000}{55261850227012}$$

Whakahekea te hautanga \frac{19073486328125000}{55261850227012} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x=\frac{4768371582031250}{13815462556753}$$