qanda-logo
search-icon
Symbol
apple-logo
google-play-logo

Calculator search results

Formula
Solve the equation
Answer
circle-check-icon
expand-arrow-icon
expand-arrow-icon
$9 ^{ 3 } +9 ^{ 3 } +9 ^{ 3 } = 3 ^{ b }$
$b = 7$
Solve the equation
$\color{#FF6800}{ 9 } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 9 } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 9 } ^ { \color{#FF6800}{ 3 } } = \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ b } }$
$ $ Invert the left and right terms to solve the exponential equation (inequality) $ $
$\color{#FF6800}{ b } = \log _{ \color{#FF6800}{ 3 } } { \left( \color{#FF6800}{ 9 } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 9 } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 9 } ^ { \color{#FF6800}{ 3 } } \right) }$
$b = \log _{ 3 } { \left( \color{#FF6800}{ 9 } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 9 } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 9 } ^ { \color{#FF6800}{ 3 } } \right) }$
$ $ Add the forms of the powers with the same bases and exponents $ $
$b = \log _{ 3 } { \left( \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 9 } ^ { \color{#FF6800}{ 3 } } \right) }$
$b = \log _{ 3 } { \left( \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 9 } ^ { \color{#FF6800}{ 3 } } \right) }$
$ $ Simplify the expression $ $
$b = \log _{ 3 } { \left( \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 729 } \right) }$
$b = \log _{ 3 } { \left( \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 729 } \right) }$
$ $ Multiply $ 3 $ and $ 729$
$b = \log _{ 3 } { \left( \color{#FF6800}{ 2187 } \right) }$
$b = \log _{ 3 } { \left( \color{#FF6800}{ 2187 } \right) }$
$ $ Write the number in exponential form with base $ 3$
$b = \log _{ 3 } { \left( \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 7 } } \right) }$
$b = \log _{ \color{#FF6800}{ 3 } } { \left( \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 7 } } \right) }$
$ $ Simplify the expression using $ \log_{a}{a^{x}}=x\times\log_{a}{a}$
$b = \color{#FF6800}{ 7 } \log _{ \color{#FF6800}{ 3 } } { \left( \color{#FF6800}{ 3 } \right) }$
$b = 7 \log _{ \color{#FF6800}{ 3 } } { \left( \color{#FF6800}{ 3 } \right) }$
$ $ The logarithm is equal to 1 if a base is same as an antilogarithm $ $
$b = 7 \times \color{#FF6800}{ 1 }$
$b = 7 \color{#FF6800}{ \times } \color{#FF6800}{ 1 }$
$ $ Multiplying any number by 1 does not change the value $ $
$b = \color{#FF6800}{ 7 }$
Have you found the solution you wanted?
Try again
Try more features at Qanda!
Search by problem image
Ask 1:1 question to TOP class teachers
AI recommend problems and video lecture
apple-logo
google-play-logo