G33k
  • G33k
i needed to edit this question :p
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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SolomonZelman
  • SolomonZelman
Are you aware of the fact that (for instance) \(\color{#000000 }{ \displaystyle \log_{134}(134)=1 }\) and of that (for instance) \(\color{#000000 }{ \displaystyle \log_{2}(8)=\log_2(2^3)=3\times \log_2(2)=3\times 1 =3 }\)
SolomonZelman
  • SolomonZelman
These examples come out from some properties that logarithmic functions satisfy... Precisely, in your problem, you need to know that: ■ Rule 1: \(\color{#000000 }{ \displaystyle \log_a(a)=1 }\) (This is true for all positive \(a\), besides a=1) ■ Rule 2: \(\color{#000000 }{ \displaystyle \log_b(a^c)=c\times \log_b(a) }\) Regardless of the base (as long as base is valid), the exponent inside the logarthm is going to go outside the logarithm, but this is true if the entire part of the log is raised to the exponent. So I can say \(\color{#0000ff }{ \displaystyle \log_b(a^c)=c\times \log_b(a) }\) But I can NOT say \(\color{#ff0000 }{ \displaystyle \log_b(a^c+x)=c\times \log_b(a+x) }\) (And for this rule, a and b can be the same number as well.)
SolomonZelman
  • SolomonZelman
And the hint: \(\color{#000000 }{ \displaystyle 49=7\times 7=7^2 }\) Which should complete the understanding...

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SolomonZelman
  • SolomonZelman
you have log\(\color{red}{_7}\)(49). And this is not 7.
SolomonZelman
  • SolomonZelman
I don't want to sound impolite, but have you read what I wrote regarding your problem (examples, rules and the hint)?
SolomonZelman
  • SolomonZelman
yw

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