9. Solve each logarithmic equation. Identify and reject any extraneous roots log(x + 11) – 1 = log 4 log, x + log4(x – 30) = 3

Q: 13. Combine the following into a logarithm: single 2 log – 3 log y + log(x*y²)

A:

Q: Given that logx = -2 and logy = 3 then simplified value of log(x7 * y³) is 29 -5 32 15 None of these

A: Given: logx = -2 and logy=3 To evaluate: logx7×y3 We know the following logarithm properties logmn=…

Q: 15) Use the properties of logarithms to rewrite each 2 a. In c. In 5y b. In Vr+2 d. In ¤(x +1)´

A: Explanation and solutions is given below....

Q: Find a number E such that log (5z + 1) = 2

A: The solution is given below.

Q: 2-Solve the following logarithmic equations. a) Log, 2 – log 4 b) 2 + 5(3*) =3(3*) x +7/6=0 -

A: We have to solve the given logarithmic equations to find the value of the variable x. For this, we…

Q: Find the largest value of x that satisfies: loge (2) – log,(r + 1) = 6

A: Use the properties of logarithmic function, to rewrite the given equation.…

Q: Solve the following: 2x-6 = 1            8   log5 (x+3)=1-log5 (x-1)

A: Using definition & rules of logarithm.

Q: If loga = logx – 2(logy + logz), then a is equal to O Ax-y²z? В. Х v²z? O C.x-2y+2z OD. X 2y +2z

A: given,

Q: how do i condense this expression to a single logarithm? step by step please

A: The given logarithmic expression is

Q: 23. Solve for x: a) log, (x- 5) + log,(x - 2) = 2 b) 5*+2 - --2500

A:

Q: If  x is an integer then solve (log2x)2-logx4 - 32 = 0

A: The given equation is (log2x) 2 -logx4 - 32 = 0

Q: Solve the following: 1 (1) 2*-6 8 (ii) log,(x+3)=1- log,(x-1) =-

A:

Q: 3. Expand the logarithms below: log,(3x'y^y' b. log log (– 2a²b*)* а.

A: Solution:  The objective is to expand the given logarithmic functions

Q: 12.) Use the laws of logarithms to combine: 2 log x + 1 log(x² + 1)

A: We have to use the laws of logarithms for the given equation.…

Q: 9⋅7x=3.5e^(2x) Find x using natural log

A: Given exponential equation is:Solve for x using natural log.

Q: 9. Condense (log4x – log4y)+2 log4(x+1) into a single logarithm with a coefficient of one.

A: Explanation of the answer is as follows

Q: Solve the following logarithm problem for the positive solution for x. 1 log, x = 2

A: Given, log4x=-12

Q: 4. Solve the following using logarithms. a) log x + log(x - 1) = log 2 b) log 40 - log10 = logx

A:

Q: at any point h (1, 1) is logx – x

A:

Q: Show that if x is positive, then

A: To prove: loge1+1x>11+x

Q: , Find the solution for x: log (Vz+1+1) log V- 40

A: See the details solution in below

Q: log (x2) - log(v9) + log(z4) condensed into a single logarithm is expressed as log() Select one: O…

A: Expression is given by logx2 - logy + logz4 To evaluate : Single logarithmic expression.

Q: 12. Solve the following equation * 3 poin log, x + log, (x -9)= 2 O 12 О 3, 12 О з 8. O -8 O -2, 8 O…

A: We use the formula logam + logan = loga(mn) logab = c    →  b = ac

Q: Given that y = log, 11 and 64 %3D x = log 2, what is logp expressed in terms of x and y? a. 2х-бу b.…

A: We are given that y=logb11 and x=logb2. We need to find what is logb64121 in terms of x and y. Now,…

Q: 2-Solve the following logarithmic equations a) Log, 2 – log 4 x +7/6=0 b) 2 + 5(3*) =3(32*)

A: logx2-log4x+76=0log2logx-log4x+76=01logxlog2-log4x+76=012logx2log2-log4x+76=012logxlog22-log4x+76=01…

Q: Express the given quantity as a single logarithm In(x 2)7 In x In(x23x 2)2 2

A: Make the coefficients into exponent. And they will multiply with the existing exponents.

Q: Find the largest value of x that satisfies: log, (22) – log2(x +1) = 2

A:

Q: 5. (a) Solve for x, if log1o(10x + 20)- log10(2x-6) = 1 (b) Given that log10 7 = 1.473, find without…

A:

Q: Express the following logarithms in terms of ln 2 and ln 3. ln 3√2

A: Solution:- the given term is A=ln(32) as we know that  ln(m×n)=lnm+lnnand ln(a)b=bln(a)

Q: Expand the logarithmic expression In(XY^2Z^3)

A: To expand the logarithmic expressionlnxy2z3

Q: Solve the following logarithmic equations. a) log2 (x) + log2(x +2) = log2(x + 12). In(x) + In(x -…

A: By Using logarithmic formula

Q: 4. Find all the values of z for which each equation holds. (a) Log(z - 1) = -i.

A:

Q: The solution of the logarithmic equation log z + log(x + 5) = log 24 is 3. 11 O16

A:

Q: 3. 9. a) Solve for x: log4 xX = b Write as a single log: 2log, 3x + 3log5y – 4log5z

A:

Q: (a) Solve the following: 1 (i) 2-6 8. (ii) log, (x+3) =1– log,(x–1)

A:

Q: 11. What are the approximate solutions to log(4x − 1) - x≈ 2.95, x≈ 2.00 x≈ 1.75, x≈ 24.83 Ox0.25, x…

A:

Q: B. Convert to an exponential equation. 1. log, T =x 2. t= log, 7 3. In 0.38 =- 0.9676 5. log 0.01 =-…

A:

Q: . Use the Laws of Logarithms to expand the expression.

A: We have to use the laws of logarithms to expand the expressions: a logxy3z2      b lnxy     c…

Q: (a) Solve the following: -1 (i) 2*-6 8 (ii) log, (x+3) = 1– log, (x-1)

A: An equation is a formula that provides the equality of two expressions, by connecting them with the…

Q: 7. Solve each equation for y. [Leave final answers in a simplified exact form or an approximate…

A: Given, (a)  ln4y +5  = lny-1  (b) 5-3log4x-3 = -4 We have to solve the equations

Q: Expand the logarithm fully using the properties of logs. Express the final answer in terms of log x,…

A: Explanation of the answer is as follows

Q: given log y+3 log(x+2): REWRITE as a single log

A:

Q: (b) Find the value of x: log ; x - log ; Vx = log 9- log ; 3

A: Basic concepts: remember these properties:

Q: 2. Rewrite in terms of a single log (condense): (15log. (x) + 10log. (v)]– 7[3lo9. (x) + loga (v)] 5

A:

Q: Solve the following logarithmic inequalities. 1. log5x 2 3. log273 > x 4. log2(5x + 7) > 5 5.…

A:

Q: b) Find the value of x that satisfies log(x+3)− log x = log x+log 2.

A: Follow the procedure given below.

Q: 12.) Use the laws of logarithms to combine: 1 2 log x log(x² + 1) - 2

A: