Logarithm Help Please

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[cosmic onyx]

I don't know how to do 2a and no video is helping

[quasi violet]

ok

do you understand the log laws?

$4\log_q (3) + 2\log_q (2) - \log_q (144) = 2$

[tawny lintel]

imdeadinside4630

[quasi violet]

This statement is equal to

$\log_q (3^{4}) + \log_q (2^{2}) - \log_q (144) = 2$

[tawny lintel]

imdeadinside4630

[quasi violet]

which is equal to

$\log_q (3^{4} * 2^{2}) - \log_q (144) = 2$

[tawny lintel]

imdeadinside4630

[quasi violet]

And

$\log_q (\frac {81*4}{144}) = 2$

[tawny lintel]

imdeadinside4630

[quasi violet]

$\log_q (2.25) = 2$

[tawny lintel]

imdeadinside4630

[quasi violet]

so

$q = \sqrt {2.25}$

[tawny lintel]

imdeadinside4630

[quasi violet]

1.5 or -1.5

[opaque fulcrum]

q>0

[quasi violet]

right