Question

log4(16x^2y^5/z^4t^8)

rewrite in terms of multiple logarithms of single variables

Answer 1

\[\log_{4}16+\log_{4}x^2+\log_{4}y^5-\log_4{z^4}-\log_{4}t^8\]
\[=2+2\log_{4}x+5\log_{4}y-4\log_{4}z-8\log_{4}t\]

Answer 2

\[\log_aMN=\log_aM+\log_aN\]
\[\log_a\frac{M}{N}=\log_aM-\log_aN\]

Answer 3

thanks dock

can you rewrite this as a single logarithm

2ln(4)-4ln(x)+1/2ln(y)-4ln(z)+6ln(w)+3ln(t)

Answer 4

use the rules above

Answer 5

\[\ln(x)=\log_e(x)\]

Answer 6

is it ln(16 * sqrty*x^4/z^4*w^6*t^3)

Answer 7

x^4 should be in the denominator

Answer 8

w^6 in the numerator

Answer 9

t^3 in the numerator

Answer 10

it would be easier if you arranged it so all of the addition is on the left, all of the subtraction is on the right