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log_(2)(4x-3)+log_(2)(3x+5)=

log⁡2(4x−3)+log⁡2(3x+5)= \log _{2}(4 x-3)+\log _{2}(3 x+5)=

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Properties of logarithms: mixed reviewright chevron icon

Full solution

Q. log⁡2(4x−3)+log⁡2(3x+5)= \log _{2}(4 x-3)+\log _{2}(3 x+5)=
  1. Combine Logarithms: Combine the two logarithms using the product rule for logarithms, which states that log⁡b(m)+log⁡b(n)=log⁡b(mn)\log_b(m) + \log_b(n) = \log_b(mn).log⁡2((4x−3)(3x+5))\log_{2}((4x-3)(3x+5))
  2. Expand Product: Expand the product (4x−3)(3x+5)(4x-3)(3x+5).4x×3x+4x×5−3×3x−3×54x \times 3x + 4x \times 5 - 3 \times 3x - 3 \times 512x2+20x−9x−1512x^2 + 20x - 9x - 15
  3. Combine Like Terms: Combine like terms in the expanded expression. 12x2+11x−1512x^2 + 11x - 15
  4. Write Single Logarithm: Write the combined expression as a single logarithm. log⁡2(12x2+11x−15)\log_{2}(12x^2 + 11x - 15)

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