Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve the following logarithm problem for the positive solution for
x.

log_(x)5=(1)/(2)
Answer:

Solve the following logarithm problem for the positive solution for $x$ . $\newline$ $\log _{x} 5=\frac{1}{2}$ $\newline$ Answer:

View step-by-step help

View step-by-step help

Quotient property of logarithms

Full solution

Q. Solve the following logarithm problem for the positive solution for

x

.

\newline

\log _{x} 5=\frac{1}{2}

\newline

Answer:

Understand the logarithmic equation: Understand the logarithmic equation. $\newline$ The equation $\log_{x}5 = \frac{1}{2}$ means that $x$ raised to the power of $\frac{1}{2}$ equals $5$ . We need to find the value of $x$ that satisfies this equation.
Convert to exponential form: Convert the logarithmic form to exponential form. $\newline$ Using the definition of a logarithm, we can rewrite the equation in its exponential form: $x^{\frac{1}{2}} = 5$ .
Solve for x: Solve for x. $\newline$ To find $x$ , we need to get rid of the exponent $\frac{1}{2}$ . We can do this by raising both sides of the equation to the power of $2$ , which is the reciprocal of $\frac{1}{2}$ . $\newline$ $(x^{\frac{1}{2}})^2 = 5^2$ $\newline$ $x = 25$

More problems from Quotient property of logarithms

Question

13 \mathrm{~km}

stretch of road needs repairs. Workers can repair

3 \frac{1}{2} \mathrm{~km}

of road per week.

\newline

How many weeks will it take to repair this stretch of road?

\newline

Posted 10 months ago

Question

Liam opened a savings account and deposited

\$ 6000

. The account earns

5 \%

in interest annually. He makes no further deposits and does not withdraw any money. In

t

\$ 8865

in this account.

\newline

Write an equation in terms of

t

that models the situation.

Posted 10 months ago

Question

Samantha opened a savings account and deposited

\$ 8192

. The account earns

10 \%

in interest annually. She makes no further deposits and does not withdraw any money. In

t

\$ 25,710

in this account.

\newline

Write an equation in terms of

t

that models the situation.

Posted 10 months ago

Question

The graph of a sinusoidal function intersects its midline at

(0,-7)

and then has a minimum point at

\left(\frac{\pi}{4},-9\right)

\newline

Write the formula of the function, where

x

is entered in radians.

\newline

f(x)=

Posted 10 months ago

Question

The following formula is used in economics to find a company's gross profit rate

P

S

is the net sales and

C

is the cost of goods sold.

\newline

P=\frac{S-C}{S}

\newline

Rearrange the formula to highlight the cost of goods sold.

\newline

C=\square

Posted 10 months ago

Question

3 \cdot 5^{0.2 w}=720

\newline

What is the solution of the equation?

\newline

Round your answer, if necessary, to the nearest thousandth.

\newline

w \approx

Posted 10 months ago

Question

18 \cdot 2^{5 t}=261

\newline

What is the solution of the equation?

\newline

Round your answer, if necessary, to the nearest thousandth.

\newline

t \approx

Posted 10 months ago

Question

-4 \cdot 3^{6 w}=-1750

\newline

What is the solution of the equation?

\newline

Round your answer, if necessary, to the nearest thousandth.

\newline

w \approx

Posted 10 months ago

Question

20 \cdot 7^{3 y}=5

\newline

What is the solution of the equation?

\newline

Round your answer, if necessary, to the nearest thousandth.

\newline

y \approx

Posted 10 months ago

Question

10 \cdot 3^{\frac{5 t}{4}}=800

\newline

What is the solution of the equation?

\newline

Round your answer, if necessary, to the nearest thousandth.

\newline

t \approx

Posted 10 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant