Question

please send answer of this page step by step ​

Answer 1

Answer:

Explanation:

Exponential equations are equations in which variables occur as exponents.

For example, exponential equations are in the form ax=by .

To solve exponential equations with same base, use the property of equality of exponential functions .

If b is a positive number other than 1 , then bx=by if and only if x=y . In other words, if the bases are the same, then the exponents must be equal.

Example 1:

Solve the equation 42x−1=64 .

Note that the bases are not the same. But we can rewrite 64 as a base of 4 .

We know that, 43=64 .

Rewrite 64 as 43 so each side has the same base.

42x−1=43

By the property of equality of exponential functions, if the bases are the same, then the exponents must be equal.

2x−1=3

Add 1 to each side.

2x−1+1=3+12x=4

Divide each side by 2 .

2x2=42x=2

 

Note:

If the bases are not same, then use logarithms to solve the exponential equations. See Solving Exponential Equations using Logarithms .