Question

Solve each exponential equation. round your answer to two decimal places.

4a. 4²x +3=1

4b. ex-1 -5 = 5

Answer 1

You have writing errors may be

`\\ \rm\Rrightarrow 4x²+3=1`

`\\ \rm\Rrightarrow 4x²=1-3`

`\\ \rm\Rrightarrow 4x²=-2`

`\\ \rm\Rrightarrow x^2=-1/2`

`\\ \rm\Rrightarrow logx²=-log0.5`

`\\ \rm\Rrightarrow 2logx=-log0.5`

`\\ \rm\Rrightarrow logx=0.15`

`\\ \rm\Rrightarrow x=10^(0.15)`

`\\ \rm\Rrightarrow x=1.412`

#2

`\\ \rm\Rrightarrow e^(x-1)-5=5`

`\\ \rm\Rrightarrow e^(x-1)=10`

`\\ \rm\Rrightarrow x-1=ln10`

`\\ \rm\Rrightarrow x-1=2.3`

`\\ \rm\Rrightarrow x=2.3+1`

`\\ \rm\Rrightarrow x=3.3`

Answer 2

4a.4²x +3=1

Slotuion:

4²x + 3=1 : x= -⅛ (Decimal:x= -0.125)

Steps

4² x +3=1

4²=16

16x + 3=1

Subract 3 from borh sides

16x +3-3=1-3

Simplify

16x=-2

Divides both sides by 16

`(16 * )/(16) = </p><p>[tex] ( - 2)/(16)`

[/tex]

Simplitfy

`(16 * )/(16) : x`

Simplify

`( - 2)/(16): -⅛`

x = -⅛

therefore the answer is x= -⅛

4b.ex-1 -5 =5

x~=3.30258

Step-by-step explanation:

e^(x-1)-5=5

e^(x-1)=10

x-1=ln 10

x-1~=2.30258

x~=3.30258

`\large \pink{ \overbrace{ \underbrace{ \tt{ \color{red}{ \: \: \: \: \: \: \: hope \: it \: help \: you \: \: \: \: \: \: \: \: }}}}}`