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how do you solve exponential Expression w/ (STEP BY STEP)?

EXAMPLE:

Solve the exponential equation 7y + 1 = 343y.

Solution:

343 + 73 is a known number. This allows the given equation to be expressed as,

7y + 1 = (73)y

7y + 1 = 73y

The bases are now the same on both sides. We can therefore set the exponents to the same value.

y + 1 = 3y

Taking y away from both sides,

2y = 1

by 2, divide both sides.

y = 1/2

Therefore, the exponential equation 7y + 1 = 343y is y = 1/2

An exponential equation is one with exponents where one or more of the exponents is a variable. Examples of exponential equations include 4x = 81, 5x - 3 = 625, 62y - 7 = 121, etc. When attempting to solve problems involving algebra, compound interest, exponential growth, exponential decay, etc., we might employ exponential equations.

Different Exponential Equation Types

Exponential equations come in three varieties. Here are some of them:

• Equations with identical bases on either side. 4x = 42, for instance.
• Equations that may be made to have the same value using various bases. (For instance, 4x = 16 is equal to 4x = 42.)
• Different-base equations that cannot be made to have the same value. (4x = 15, for instance).

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