Question

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

Answer 1

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

$\frac{16 \times }{16} = [tex] \frac{ - 2}{16}$

[/tex]

Simplitfy

$\frac{16 \times }{16} : x$

Simplify

$\frac{ - 2}{16}: -⅛$

x = -⅛

therefore the answer is x= -⅛

4b.ex-1 -5 =5

x~=3.30258

explanation:

e^(x-1)-5=5

e^(x-1)=10

x-1=ln 10

x-1~=2.30258

x~=3.30258

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Answer 2

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

$\\ \rm\Rrightarrow e^{x-1}-5=5$

$\\ \rm\Rrightarrow e^{x-1}=10$

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

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

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

$\\ \rm\Rrightarrow x=3.3$