How do you simplify and solve #(4^(2x)+3) + (4^(2x)+2) = 320#?

Answer 1

Genesis Allen

#4^(2x) *2=315#

#-> 4^(2x) = 315/2#

#->ln(4^(2x)) = ln(315/2)#

#->2xln(4)=ln(157.5)#

#->2x=ln(157.5)/ln(4)#

#-> 2x ~=3.64#

#-> x~=1.82#

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Answer 2

Abigail Allen

Have a look:

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Answer 3

Genesis Allen

To simplify and solve the equation ( (4^{2x}+3) + (4^{2x}+2) = 320 ):

Combine like terms: ( 2(4^{2x}) + 5 = 320 ).
Subtract 5 from both sides: ( 2(4^{2x}) = 315 ).
Divide both sides by 2: ( 4^{2x} = 157.5 ).
Take the natural logarithm of both sides: ( \ln(4^{2x}) = \ln(157.5) ).
Apply the power rule of logarithms: ( 2x \cdot \ln(4) = \ln(157.5) ).
Divide both sides by ( 2 \cdot \ln(4) ) to solve for ( x ): ( x = \frac{\ln(157.5)}{2 \cdot \ln(4)} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.