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Simplify as a single log...

 2log⁡ax+3ln⁡x\ 2 \log_a x + 3 \ln x

Heres what I've done

log⁡ax2+lnx3\log_a x^2 + ln x^3 .

but I don't know how you could simply this further.
(edited 5 years ago)
Reply 1
Avatar for Notnek
Notnek
21
Original post by E--
2 loga x + 3 ln x

Heres what I've done
loga x^2 + In x^2
but I don't know how you could simply it.

Can you please post the original question? Or did it just say "simplify"?
Reply 2
Avatar for E--
E--
OP
7
Original post by 𝓝𝓸𝓽𝓷𝓮𝓴
Can you please post the original question? Or did it just say "simplify"?

It says simplify as a single log
Reply 3
Avatar for Notnek
Notnek
21
Original post by E--
It says simplify as a single log

Well you can write it as a log within a log. It's a bit of an odd question though - if there's any details you haven't posted then please do.

Start by using the change of base formula so that all your logs have the same base. Are you aware of this formula?
Reply 4
Avatar for E--
E--
OP
7
Original post by 𝓝𝓸𝓽𝓷𝓮𝓴
Well you can write it as a log within a log. It's a bit of an odd question though - if there's any details you haven't posted then please do.

Start by using the change of base formula so that all your logs have the same base. Are you aware of this formula?

log⁡ax2+lnx3\log_a x^2 + ln x^3

log⁡ax2+logex3\log_a x^2 + log_e x^3

log⁡ex3=\log_e x^3= logax3logae\frac{log_a x^3}{log_a e}

is this right?
Reply 5
Avatar for Notnek
Notnek
21
Original post by E--
log⁡ax2+lnx3\log_a x^2 + ln x^3

log⁡ax2+logex3\log_a x^2 + log_e x^3

log⁡ex3=\log_e x^3= logax3logae\frac{log_a x^3}{log_a e}

is this right?

That's right although it would have been nicer to change to base e instead of a so that you can just write ln (plus natural logs are more common).
Reply 6
Avatar for E--
E--
OP
7
Original post by 𝓝𝓸𝓽𝓷𝓮𝓴
That's right although it would have been nicer to change to base e instead of a so that you can just write ln (plus natural logs are more common).

oh ok so it will be,
log⁡ax3=\log_a x^3= logex3logea\frac{log_e x^3}{log_e a}
which gives,
log⁡ax3=\log_a x^3= x3a\frac{x^3}{a}

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