Question

2^(x+1)=5

Answer 1

can you "take the log" of both sides?

Answer 2

that means write log( ) around each side

Answer 3

Would It Be Like This 2 log (x+1) =log(5)

Answer 4

it would be like this
\[ \log\left( 2^{(x+1)}\right) = \log(5) \]

Answer 5

now use the "rule"
\[ \log(a^b) = b\ \log(a) \]

Answer 6

in your problem, a is 2 and "b" is the exponent (x+1)

Answer 7

x+1 log (2)

Answer 8

yes, but use parens around (x+1)
and write the whole equation. (Good habit to get into)

Answer 9

(x+1) log (2)=log(5)

Answer 10

though log(2) looks complicated, it is a number (like 2 or 3, for example)
divide both sides by log(2)
\[ (x+1) \frac{\log(2)}{\log(2)} = \frac{\log(5)}{\log(2)}\]

Answer 11

(x+1)=log(5)/log(2) ?

Answer 12

on the left side anything divided by itself is 1 (except 0/0)

yes , you have
\[ x+1 = \frac{\log(5)}{\log(2)} \]
add -1 to both sides

Answer 13

x=log(5)/log(2)-1

Answer 14

if you want a decimal number, you will need a calculator, or type
log(5)/log(2)-1=
into the google search window

Answer 15

So Its 1.3219?

Answer 16

roughly... the more decimals the more accurate
using 1.3219
in the original equation:

2^(1+1.3219) = 4.99990263
which is close to 5 (as it should be)

Answer 17

Awesome. Thank You!

Answer 18

yw