1. logx+log(x+48)=2
14.log50+log(x/2)=2
23.log72-log(2x/3)=0
Could someone please explain to me how to solve these?
1
32
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thanks, but how do i solve them?
remember the rule of logs?
Log (ab)= loga + logb so, take 14 as an example:
log50 + log(x/2)=2
log(50x/2)=2
50x/2= antilog2
solve for x
On 23, the formula is
log(a/b)= loga - logb
thanks!
To solve these logarithmic equations, we need to apply logarithmic properties and algebraic manipulations. Here's a step-by-step explanation for each equation:
1. logx + log(x + 48) = 2
Step 1: Combine the logarithms using the product rule of logarithms: log(A) + log(B) = log(A * B).
log(x(x + 48)) = 2
Step 2: Rewrite the equation in exponential form: If log base b of y = x, then b^x = y.
10^2 = x(x + 48)
Step 3: Simplify and solve the quadratic equation:
x^2 + 48x - 100 = 0
You can solve this quadratic equation using factorization or the quadratic formula. The solutions will provide the values of x for which the equation is true.
2. 14log50 + log(x/2) = 2
Step 1: Apply the power rule of logarithms: log(base b) of (x^n) = n log(base b) of x.
log(50^14) + log(x/2) = 2
Step 2: Simplify the logarithms using the rules of logarithms:
log(50^14 * (x/2)) = 2
Step 3: Rewrite the equation in exponential form:
10^2 = 50^14 * (x/2)
Step 4: Simplify and solve for x.
3. log72 - log(2x/3) = 0
Step 1: Apply the quotient rule of logarithms: log(A) - log(B) = log(A/B).
log(72 / (2x/3)) = 0
Step 2: Simplify the logarithm using the rules of logarithms:
log((72 * 3) / (2x)) = 0
Step 3: Rewrite the equation in exponential form:
10^0 = (72 * 3) / (2x)
Step 4: Simplify and solve for x.
Remember, after obtaining the solutions, it is always a good practice to verify if the solutions make the original equation true.