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Exponential and logarithmic equations
Undo an exponential with a logarithm, and a logarithm with an exponential.
When the unknown is in the exponent, take a logarithm of both sides; the exponent comes down as a multiplier. When the unknown is inside a log, rewrite in exponential form. Always check the domain: logarithms need positive arguments.
ຕົວຢ່າງທີ່ໄດ້ເຮັດ · 2^x = 8
ຂັ້ນຕອນຕໍ່ຂັ້ນຕອນ
- 2^{x} = 8
Start from the equation as given.
- 2^{x} - 8 = 0
Bring everything to one side.
- 2^{x} - 8 = 0
Isolate the exponential, then take a logarithm of both sides.
- x = 3
Solve for the variable.
ເປີດເຜີຍຄຳຕອບ
ປັດຈຸບັນທ່ານ ເລືອກບັນຫາ ຫຼື ພິມ ຫຼື ແຕ້ມເອງ. ທຸກບາດກ້າວ, ຮູບ, ຄໍາຕອບຖືກລົບຈົນກວ່າເຈົ້າຈະຖາມມັນ.
ຕົວສະແດງທີ່ໃຊ້ຢູ່ທີ່ນີ້
ກົດຕົວອັກສອນໃດໜຶ່ງເພື່ອເບິ່ງຄວາມໝາຍເຕັມ, ຮູບ ແລະ ຕົວອັກສອນແຕ່ລະຕົວໃນມັນໝາຍຄວາມວ່າແນວໃດ.
ວິທີການ: Exponential and logarithmic equations
- Start from the equation as given.
- Bring everything to one side.
- Isolate the exponential, then take a logarithm of both sides.
- Solve for the variable.
ຄໍາຖາມທີ່ຄົນຖາມ
What does it mean to solve an equation?
To find every value of the unknown that makes both sides equal. Each step is an operation applied to both sides that keeps the solution set the same, until the unknown stands alone.
Why do I sometimes get two answers?
A quadratic can cross the axis twice, so it can have two solutions. A degree-n polynomial has up to n. The graph shows where each one comes from.
How do I know whether to factor or use the quadratic formula?
Try factoring for a few seconds: look for two numbers that multiply to a·c and add to b. If nothing obvious appears, the discriminant b² − 4ac tells you how many real roots there are, and the formula finds them without guessing.
ເພີ່ມເຕີມໃນ Algebra
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