Question

simplify log base 4 of 1024

Answer 1

\(\large \bf log_{\color{red}{ a}}{\color{blue}{ b}}=y\iff {\color{red}{ a}}^y={\color{blue}{ b}}\qquad thus
\\ \quad \\
log_{\color{red}{ 4}}{\color{blue}{ 1024}}=\square\implies {\color{red}{ 4}}^\square ={\color{blue}{ 1024}}\quad thus \quad \square =?\)

Answer 2

\[\log_4 1024 = x\]Now you have to ask yourself, 4 to what power will equal 1024? putting that down in a formula, we have \[4^x = 1024\] In order to solve for x, we have to get 1024 to look like \(4^n\)

Answer 3

ok, thanks, i think i get it now, so im just simplifying this log into not a log?

Answer 4

\[1024 = 4 \cdot 4^4 = 4^1 \cdot 4^4 = 4^{4+1} = 4^{5}\] And yes , you're using the properties of logarithmic functions to evaluate x.

Answer 5

So I'll start you off and you can finish it! \[4^x = 4^5\] Because the bases are the same, we can simply evaluate their powers.

Answer 6

oh ok, thanks, i thought it was one of these different properties tht i learned ttoday, not ones i learned yesterday, i just had to look through my old notes, thanks

Answer 7

wouldnt it be 4^5=1024

Answer 8

No problem :) And yes, 4^5 = 1024. So x would equal?

Answer 9

the exponent 5

Answer 10

Yes :D

x = 5.

Good job!

Answer 11

thanks so much