Question

i needed to edit this question :p

Answer 1

Are you aware of the fact that (for instance)
\(\color{#000000 }{ \displaystyle \log_{134}(134)=1 }\)

and of that (for instance)
\(\color{#000000 }{ \displaystyle \log_{2}(8)=\log_2(2^3)=3\times \log_2(2)=3\times 1 =3 }\)

Answer 2

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.)

Answer 3

And the hint: \(\color{#000000 }{ \displaystyle 49=7\times 7=7^2 }\)
Which should complete the understanding...

Answer 4

you have log\(\color{red}{_7}\)(49).
And this is not 7.

Answer 5

I don't want to sound impolite, but have you read what I wrote regarding your problem (examples, rules and the hint)?

Answer 6

yw