Solve:
3^(2x+1)=12
Show your workings:
3^(2x+1) = 12
We can rewrite this as:
3^(2x) * 3^(1) = 12
(3^2)^x = 12/3
9^x = 4
Get the natural logarithm of both sides:
ln (9^x) = ln (4)
x * ln(9) = ln(4)
x = ln(4) / ln(9)
We can further simplify this as:
x = ln(2^2) / ln(3^2)
x = 2*ln(2) / [2*ln(3)]
x = ln(2) / ln(3)
Hope this helps~ `u`
take logs of both sides
log 3^(2x+1) = log 12
(2x+1)log3 = log12
2x+1 = log12/log3
2x = log12/log3 - 1
x = (log12/log3 - 1)/2
= .....
To solve the equation 3^(2x+1) = 12, we can follow these steps:
Step 1: Take the logarithm of both sides of the equation to bring down the exponent.
log(3^(2x+1)) = log(12)
Step 2: Use the logarithmic rule, log(a^b) = b * log(a), to simplify the equation.
(2x+1) * log(3) = log(12)
Step 3: Divide both sides of the equation by log(3) to isolate the variable.
2x + 1 = log(12) / log(3)
Step 4: Subtract 1 from both sides of the equation to solve for the variable.
2x = (log(12) / log(3)) - 1
Step 5: Divide both sides of the equation by 2 to obtain the final solution.
x = [(log(12) / log(3)) - 1] / 2
Now, you can use a calculator to evaluate the right-hand side of the equation to get the numerical value of x.