How do I rewrite without logarithms??
2. log x= log a - 4 log b
3. ln t= 3/2 ln a - ln p
4. log y = 3 log x + log 17
2
logx = loga - 4logb
logx= loga - log b^4
logx = log (a/b^4)
x = 1/b^4
3.
lnt = (3/2)ln a - ln p
ln t = ln ((√a)^3) - ln p
ln t = ln( (√a)^3 /p)
t = √a)^3 /p
4. you do this one the same way
of course you will have to know the rules of logs
To rewrite equations without logarithms, we can use the properties of logarithms to simplify them. Here's how you can rewrite each equation without logarithms:
1. log x = log a - 4 log b
To eliminate the logarithms, we can apply the exponentiation property of logarithms, which states that if log(base b) x = y, then x = b^y. Applying this property, we can rewrite the equation as:
x = a / (b^4)
2. ln t = (3/2) ln a - ln p
To get rid of the logarithms, we can use the property that ln(ab) equals ln(a) + ln(b). Using this property, we can rewrite the equation as:
ln t = ln(a^(3/2)) - ln p
Next, we can simplify further using the quotient rule of logarithms, which states that ln(a/b) is equal to ln(a) - ln(b). Applying this rule, we have:
ln t = ln(a^(3/2)/p)
Finally, using the property that ln(e^x) = x, the equation simplifies to:
t = (a^(3/2))/p
3. log y = 3 log x + log 17
To rewrite this equation, we can apply the logarithmic identity log(ab) equals log(a) + log(b). Using this identity, we can rewrite the equation as:
log y = log(x^3) + log 17
Next, we can further simplify using the sum rule of logarithms, which states that log(a) + log(b) is equal to log(ab). Applying this rule, we have:
log y = log(17x^3)
Finally, we can use the exponentiation property of logarithms to rewrite the equation without logarithms:
y = 17x^3
By applying these logarithmic properties and rules, we can rewrite equations without using logarithms.