# Write as a sum or difference of logarithms

• November 15th 2007, 07:22 AM
oceanmd
Write as a sum or difference of logarithms
Write as a sum or difference of logarithms:
Log b(base) 8^ (8th root)√(x^5y^3):z^9 (x, y and z under the root sign)

It’s hard to type the solution, I need to learn how to post the questions the right way, but for now please excuse me. Is the answer ⅝ log b (base) x + ⅜ log b (base) x – 9/8 log b (base) 2

Thank you
• November 15th 2007, 08:05 AM
red_dog
If you mean $\displaystyle\log_b\sqrt[8]{\frac{x^5y^3}{z^9}}$ then what you wrote is correct:
$\displaystyle\frac{5}{8}\log_bx+\frac{3}{8}\log_by-\frac{9}{8}\log_bz$.

(The last sign is z, not 2)
• November 15th 2007, 08:10 AM
oceanmd
red dog, thank you