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How do you solve #2 ^(4x)= 2.7#?

Answer 1

James Allen

#color(blue)(x=ln(2.7)/(4ln(2))~~0.3582398518)#

According to logarithmic laws:

#log_a(b^c)=clog_a(b)#

#2^(4x)=2.7#

Using both sides' natural logarithms:

#4xln(2)=ln(2.7)#

Divide by #4ln(2)#:

#x=ln(2.7)/(4ln(2))~~0.3582398518#

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Answer 2

Anna Allen

To solve the equation 2^(4x) = 2.7, you first take the natural logarithm (ln) of both sides to bring down the exponent. Then, you solve for x by isolating it. After taking the natural logarithm of both sides, the equation becomes ln(2^(4x)) = ln(2.7). Using the property of logarithms that allows the exponent to come down as a coefficient, the equation simplifies to 4x * ln(2) = ln(2.7). Finally, to solve for x, divide both sides by ln(2) to get x = ln(2.7) / (4 * ln(2)). This expression represents the value of x that satisfies the equation 2^(4x) = 2.7.

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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.