4^x+ 2^(1+2x)= 50 I know what the answer is (about 2.03), but I need help getting there!

Question

4^x+ 2^(1+2x)= 50
I know what the answer is (about 2.03), but I need help getting there!

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Nho 7 months 2021-07-26T14:28:48+00:00 1 Answers 2 views 0

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    0
    2021-07-26T14:30:44+00:00

    Step-by-step explanation:

    4ˣ + 2¹⁺²ˣ = 50

    Rewrite 4 as a power of 2.

    2²ˣ + 2¹⁺²ˣ = 50

    Factor out 2²ˣ.

    2²ˣ (1 + 2) = 50

    2²ˣ = 50/3

    Take log of both sides.

    ln(2²ˣ) = ln(50/3)

    Use exponent property.

    2x ln 2 = ln(50/3)

    Solve for x.

    x = ln(50/3) / (2 ln 2)

    Simplify.

    x = ln(50/3) / (ln 4)

    x ≈ 2.03

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