Question

Find the value of x in each of the following equations.
a)2^x-1=13
@ganeshie8

Answer 1

time to use latex @MARC_ :)

is it \(2^{x-1} = 13\) or \(2^x-1 = 13\) ?

Answer 2

\[2^{x-1}=13\] alright :)

Answer 3

looks good, here \(x-1\) is called the `logarithm` of \(13\) in base \(2\)

Answer 4

okay

Answer 5

\[2^{x-1} = 13\]

is equivalent to
\[\large x-1 = \log_2 13\]

Answer 6

add 1 both sides and you're done :
\[\large x = 1 + \log_2 13 \]

Answer 7

http://www.wolframalpha.com/input/?i=1%2Blog%282%2C13%29

Answer 8

wolfram says \[x \approx 4.7\]

Answer 9

Alternatively you may simply use the log properties to solve \(x\) :
\[2^{x-1} = 13\]
take \(\ln\) both sides :
\[ \ln (2^{x-1}) = \ln (13)\]
by using the log property \(\color{Red}{\ln(a^x) = x*\ln(a)}\) :
\[ (x-1)*\ln (2) = \ln (13)\]
\[ (x-1) = \dfrac{\ln (13)}{\ln(2)}\]
\[x = 1+\dfrac{\ln (13)}{\ln(2)}\]

Answer 10

okay i get :)

Answer 11

Thnx @ganeshie8

Answer 12

good :) remember that `logarithm` is same as the `exponent`

\[\large a^{\color{Red}{x}} = y\]

here \(\color{Red}{x}\) is called the \(\color{Red}{\text{logarithm}}\) of \(y\) in base \(a\)

Answer 13

example, we know :

\[\large 2^{\color{Red}{3}} = 8\]

here \(\color{Red}{3}\) is called the \(\color{Red}{\text{logarithm}}\) of \(8\) in base \(2\)

Answer 14

\[ \log_2 8=\color{Red}{3} \]

Answer 15

logarithm = exponent

Answer 16

Thnx for ur explaination :)

Answer 17

yw!