Solve 9⋅8^(7/x)=6
9⋅8^(7/x)=6
we'll need logs
8^(7/x) = 2/3
take logs of both sides, and use your log rules
(7/x)log8 = log (2/3)
7/x = (log2 - log3)/log8
x/7 = log8/(log2 - log3)
x = 7log8/(log2 - log3) = ...... button-pushing time
let me know what you get.
9.8^(7/x) = 6.
(7/x)*Log9.8 = Log6
Divide both sides by Log 9.8:
7/x = 0.785
X = 8.92.
To solve the equation 9⋅8^(7/x) = 6, we can follow these steps:
Step 1: Divide both sides of the equation by 9 to isolate the exponential term:
(9⋅8^(7/x))/9 = 6/9
8^(7/x) = 2/3
Step 2: Take the logarithm of both sides of the equation. You can use any logarithm, but commonly used ones are natural logarithm (ln) or logarithm with base 10:
ln(8^(7/x)) = ln(2/3)
Step 3: Apply the exponent rule for logarithms:
(7/x)ln(8) = ln(2/3)
Step 4: Divide both sides of the equation by ln(8):
(7/x) = ln(2/3) / ln(8)
Step 5: Multiply both sides of the equation by x/7 to isolate x:
((7/x)(x/7)) = (ln(2/3) / ln(8))(x/7)
1 = (ln(2/3) / ln(8))(x/7)
Step 6: Multiply both sides by 7 to eliminate x from the denominator:
7 = (ln(2/3) / ln(8))x
Step 7: Divide both sides by (ln(2/3) / ln(8)) to solve for x:
x = 7 / (ln(2/3) / ln(8))
Now you can use a calculator to evaluate the right-hand side of the equation and find the value of x.