## Problem 871

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

ex+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 bM = bN, THEN M = N.

To solve the exponential equation ex+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  x4 = 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:-

bx = a ↔ log ba = x

log 5 = -2

## Exponential Expression

Exponential Expression

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

an  =  a .a .a ……a,

n factors of a

where n is the exponent, a is the base, and an 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 = 25.

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.

25   Exponent