Question

Rewrite the expression using log a (2) and log a (5)
Log a (sqrt 1280)

Answer 1

\[\log _{a}(\sqrt{1280})\]

Answer 2

the only thing i could think of was \[\log _{a}(2^{8}) \times \log _{a}(5)\] but i don't even think thats a real answer

Answer 3

You are on the right track but you forgot that 1280 is under the square root sign. sqrt(1280) is equal to 1280^1/2. So I think that the answer would be (1/2)log_a(2^8)xlog_a(5) sorry, I can't format it nicely since I do not know how to use LaTex on here.

Answer 4

Oh doh!!! I forgot about the root

Answer 5

you have to simplify them first inside the square root sign.\[\log_{a} (1280)^{\frac{ 1 }{ 2 }}\]\[\log_{a} \left[ \left( 2^{8} \right)\left( 5 \right) \right] ^{\frac{ 1 }{ 2 }}\]\[\log_{a} \left[ \left( 2^{4} \right)\left( 5^{\frac{ 1 }{ 2 }} \right) \right]\]

since in logarithms,\[\log_{a} X + \log_{a} Y = \log_{a} XY\]then\[\log_{a} \left[ \left( 2^{4} \right)\left( 5^{\frac{ 1 }{ 2 }} \right) \right] = \log_{a} 2^{4} + \log_{a} 5^{\frac{ 1 }{ 2 }}\] if you bring down the exponent, it'll be\[4\log_{a} 2 + \frac{ 1 }{ 2 }\log_{a} 5\]

Answer 6

please check this..i'm doubting my answer...

Answer 7

no i think...i think your answer might be right and i'm a dummy

Answer 8

because the question states that you have to use \[\log_{a}(2)and \log_{a}(5)\] in the answer.