solve 9^(2x-3) > 4. Round your answer to the nearest hundredth.
The part in parenthesis is up at top like an exponent. I dont' know how to do this. Please help me.
find the value of x such that
9^(2x-3) = 4
ln both sides
(2x-3) ln9 = ln4
2x-3 = ln4/log9
2x = 3 + ln4/ln9
x = (3 + ln4/ln9)/2 = appr 1.82
so x > 1.82
check:
let x = 1.81
LS = 9^(.62) = 3.905..... < 4
let x = 1.83
LS = 9^(.66) = 4.26.. > 4
Ah, thank you so much!!! GOd bless you!
To solve the inequality 9^(2x-3) > 4, we need to isolate the variable x. Here's how you can do it step by step:
Step 1: Take the logarithm (base 9) of both sides of the inequality. This will help us bring down the exponent.
log9(9^(2x-3)) > log9(4)
Step 2: Use the logarithmic property that loga(b^c) = c * loga(b). Applying this property to the left side of the inequality:
(2x - 3) * log9(9) > log9(4)
Step 3: Simplify the equation further:
(2x - 3) * 1 > log9(4)
2x - 3 > log9(4)
Step 4: Evaluate the logarithm using the change of base formula:
log9(4) = log(4)/log(9)
Therefore, 2x - 3 > log(4)/log(9)
Step 5: Solve for x by isolating the variable:
2x > log(4)/log(9) + 3
x > (log(4)/log(9) + 3) / 2
Step 6: Use a calculator to evaluate the right side of the inequality, where log represents the logarithm with base 10:
x > (log(4)/log(9) + 3) / 2
x > (0.6021/0.9542 + 3) / 2
x > (0.63 + 3) / 2
x > 3.315/2
x > 1.657
Finally, rounding to the nearest hundredth, x > 1.66.
Therefore, the solution to the inequality 9^(2x-3) > 4 is x > 1.66.