when I have .5=(0.91)^t, could i do
log(.5)/log(0.91) ?
yes ... that would equal t
Your answer is correct, but you also can write:
log ( x ^ n ) = n ∙ log ( x )
0.5 = 1 / 2 = 1 / 2 ^ 1 = 2 ^ ( - 1 )
log ( 0.5 ) = log [ 2 ^ ( - 1 ) ] = ( - 1 ) * log ( 2 ) = - log ( 2 )
log ( 0.91 ^ t ) = t ∙ log ( 0.91 )
0.5 = 0.91 ^ t
log ( 0.5 ) = log ( 0.91 ^ t )
- log ( 2 ) = t ∙ log ( 0.91 ) Divide both sides by log ( 0.91 )
- log ( 2 ) / log ( 0.91 ) = t
t = - log ( 2 ) / log ( 0.91 )
ok thanks!
Yes, you can use logarithms to solve the equation .5 = (0.91)^t. The logarithm of a number is the exponent to which another fixed value, called the base, must be raised to produce that number. In this case, you can use logarithms to find the value of t.
To solve the equation, you can take the logarithm of both sides. However, it's important to note that you can use any base for the logarithm, although commonly used bases are 10 (log base 10) and e, where e is Euler's number (natural logarithm, represented as ln).
Here are the steps to solve the equation:
1. Take the logarithm of both sides:
ln(0.5) = ln((0.91)^t)
2. Apply the properties of logarithms. Using the property log(a^b) = b*log(a), we can rewrite the equation as:
ln(0.5) = t * ln(0.91)
3. Divide both sides of the equation by ln(0.91) to solve for t:
t = ln(0.5) / ln(0.91)
So, using the natural logarithm, you can solve .5 = (0.91)^t by calculating t = ln(0.5) / ln(0.91).