## Posts Tagged ‘Exponential’

## Problem 871

Solve the following exponential equation by expressing each side as a power of the same base and then equating exponents.

e^{x+11} = .

**Solution:-**

An exponential equation is an equation containing a various in an exponent. Some exponential equations can be solved by expressing each side of the equation as a power of the same base.

All exponential functions are one-to-one. That is, two different ordered pairs have the same second component. Thus, if is a positive number other than 1 and b^{M }= b^{N}, THEN M = N.

To solve the exponential equation e^{x+11 }= , first express both sides of the equation as a power of the same base.

e ^{x+11 } =

e ^{x+11 } = e^{-1}

Then, set the exponents equal to each other and solve for x.

x + 11 = -1

x = -12

Therefore, the solution set is {-12}.

## Problem 696

Change the exponential statement x^{4} = 2 into an equivalent logarithmic statement.

Solution:-

= 2

taking log both sides

log = log 2

4log x= log 2

=4

## Problem 692

Change the exponential statement 5^{-2 }= into an equivalent logarithmic statement.

**Solution:-**

b^{x} = a ↔ log b^{a} = x

log 5 = -2

## Exponential Expression

**Exponential Expression**

If *a *is a real number and *n *is a natural number,

** a^{n} **=

*a .*

*a .*

*a ……*

*a***,**

*n *factors of *a*

where *n *is the **exponent, ***a *is the **base, **and *a ^{n} *is an

**exponential expression.**

Exponents are also called **powers.**

** **

For example, the product **2 . 2 . 2 . 2 . 2** is written

**2 **. **2 **. **2 **. **2 **. **2 **= **2 ^{5}**.

5 factors of **2**

The number 5 shows that 2 is used as a factor 5 times. The number 5 is the

**exponent, **and 2 is the **base.**

**2 ^{5} ←**

**Exponent**