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u0860867
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UnkleRhaukus
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\[\log_7M=\frac{\log_910-\log_95}{\log_97}\]
UnkleRhaukus
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first use this log law in the numerator of the right hand side \[\boxed{\log_b x-\log_by=\log_b\frac xy}\]
u0860867
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yeah i did that so i got log 2
UnkleRhaukus
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now use the change of base formula
\[\large\boxed{\log_b x=\frac{\log_c x}{ \log_c b}}\]
u0860867
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0.31 for the numerator
UnkleRhaukus
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leave it in log form
u0860867
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ok
UnkleRhaukus
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So you have \[\log_7M=\frac{\log_92}{\log_97}\]
comparing with the change of base formula
\[\boxed{\log_b x=\dfrac{\log_c x}{ \log_c b}}\]
we see that \(M= ~ . . .\)
u0860867
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so will u get Log7M= 0.35 @UnkleRhaukus
u0860867
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so will M =2 ?????
UnkleRhaukus
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dont convert to decimal
UnkleRhaukus
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yeah that's it M=2