Make into one log function:
2logx-log4-log3+logx
2logx-log4-log3+logx
= log (x^2) - log4 + logx
= log( x^3/4)
why did I not see that -log3 in there ??
correct answer ....
log ((x^2)(x)/((4)(3))
= log (x^3/12)
To simplify the expression and combine the logarithmic terms into one, we can start by using the logarithmic properties:
1. 2logx - log4 - log3 + logx
Using the power rule of logarithms, we multiply the coefficient outside the logarithm to the exponent inside the logarithm:
2logx = log(x^2)
Using the quotient rule of logarithms, we can combine the logarithms with a subtraction operation as:
log4 - log3 = log(4/3)
Now our expression becomes:
log(x^2) - log(4/3) + logx
Using the addition rule of logarithms, we can combine the logarithms with an addition operation as:
log(x^2) + logx - log(4/3)
Using the product rule of logarithms, we can simplify further as:
log(x^2 * x) - log(4/3)
Now our expression becomes:
log(x^3) - log(4/3)
Finally, using the quotient rule of logarithms, we can combine the logarithms with a subtraction operation as:
log(x^3 / (4/3))
Putting it all together, our simplified expression is:
log((3x^3) / 4)