Question

exponential equations
2 ^ x-1 = 3

Answer 1

if you are trying to solve for x use logs

Answer 2

\[2 ^{x-1} = 3\]

Answer 3

how

Answer 4

Use this rule:
\[\log_a(a^x) = x\]

Answer 5

Log(x) = y

is the same as

x = 10^(y)

Answer 6

could you demonstrate please

Answer 7

\[\log_{10}(x) = \log(x)\]

just note that when you see log with no base it means log base 10

Answer 8

how about in my problem ?

Answer 9

if you can use my problem as an example i could figure out the rest of my questions

Answer 10

\(\bf 2 ^{x-1} = 3\\ \quad \\
\textit{log cancellation rule of }{\color{blue}{ log_aa^x=x}}\\ \quad \\
log_2(2 ^{x-1}) = log_23\implies x-1=log_23\)

Answer 11

sure,

55^x = 55
\[\log_{55}(55^x) = \log_{55}(55)\]
\[x = \log_{55}(55)\]

Answer 12

x = 1

Answer 13

the log cancellation rule idea being, the log base, and the base of the inner quantity, being equal

Answer 14

thank you

Answer 15

\(\bf \textit{log cancellation rule of }{\large \color{blue}{ log_{\color{red}{ a}}{\color{red}{ a}}^x=x}}\)

Answer 16

Take log base 10, not log base 2... you can't solve log base 2 of 3 without using change of base formula

Answer 17

Just to note, x = 1 because,

\[\log_{55}(55^1) = \log_{55}(55) = 1\]

Answer 18

Or take natural logs of both sides.

Answer 19

natural logs of both sides\[\Large \ln 2 ^{x-1} = \ln 3\]bring down the exponent\[\Large (x-1)* \ln 2 = \ln 3\]then divide both sides by ln 2 and then just add 1 to both sides

Answer 20

oh yeah that rule,

\[\ln(a^x) = (x)\ln(a)\]

Note,

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

e is Euler's number get use to seeing it

Answer 21

oops, made a mistake,

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

Answer 22

PLEASE IGNORE the \[\ln_e(x) = \ln(x)\] that is incorrect

Answer 23

well actually maybe not, to be honest not to sure if that notation is accepted, probably not

Answer 24

though