Respuesta :

r3t40
Hi,

Work:

Equation;

[tex] {4}^{2x + 3} = 1[/tex]

Write the number in exponential form with a base of 4.

[tex] {4}^{2x + 3} = 4^{0} [/tex]

Since the bases are the same, set the exponents equal.

[tex]2x + 3 = 0[/tex]

Move constant +3 to the right side and change its sign.

[tex]2x = - 3[/tex]

Divide both sides of equation by 2.

[tex]x = - \frac{3}{2} \: \: \: \: \: \: \: result \: (fraction) \\ \\ x = - 1.5 \: \: \: \: \: \: \: \: result \: (decimal)[/tex]

Hope this helps.
gmany

[tex]4^{2x+3}=1\ \ \ \ \ |\log_4\\\\\log_44^{2x+3}=\log_41\\\\\boxed{use\ \log_a1=x\to x=0\ and\ \log_ab^n=n\log_ab}\\\\(2x+3)\log_44=0\\\\\boxed{use\ \log_aa=1}\\\\2x+3=0\ \ \ \ |-3\\\\2x=-3\ \ \ \ |:2\\\\\boxed{x=-1.5}[/tex]

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