Given the exponential equation 3x = 243, what is the logarithmic form of the equation in base 10?

1 answer:

6 0

The answer is $x= \frac{log_{10} (243 )}{log_{10} (3 )}$

$3^{x} =243$
Logarithm both sides of the equation:
$log_{10} (3^{x} ) = log_{10} (243 )$
Since: $log (a^{b}) = b*log(a)$ , then: $log_{10} (3^{x} ) =x*log_{10} (3 )$
Back to our equation:
$log_{10} (3^{x} ) = log_{10} (243 ) \\ 
x*log_{10} (3 ) = log_{10} (243 ) \\ 
x= \frac{log_{10} (243 )}{log_{10} (3 )}$

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Step-by-step explanation:

Given:

Three side length of triangle are given we need find the which value to substitute for a, b, c in Pythagoras theorem.

First we will find the squares of all length, then we will check which two square of side are equal to square of third side as per Pythagoras theorem.

Hence the two side would according be a and b and third side will become c.

For example if length of triangle is given as 6 cm, 8 cm and 10 cm.

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$6^2=36\\8^2=64\\10^2=100$