Question

please help

Exponential and Logarithmic Equations
solve each equation. Give an exact solution.
3^(4x+1)-5=22

Answer 1

start by adding 5 on both sides

Answer 2

3^(4x+1)=27

Answer 3

yes, now you can take log on both sides.
what do you get ?

Answer 4

Alternative way : write 27 as an exponent of 3 and compare the exponents

Answer 5

can you use draw cus im lost

Answer 6

\(\Large 3^{4x+1} = 27 \\ \large \log (3^{4x+1}) = \log 27 \)

Answer 7

log shmog

Answer 8

now use the log property that
\(\log a^b = b \log a\)

Answer 9

\[\large 3^{4x+1}=3^3\iff 4x+1=3\]

Answer 10

^ and there's your alternative way

Answer 11

\[4x+1\log_{3}=\log_{27} \]

Answer 12

arg

Answer 13

since \(27=3^3\) you know \(4x+1=3\)

Answer 14

x=1/2

Answer 15

yeah, but did you get how ?

Answer 16

yes