Question

Solve for x

$\boxed{\sf log_5(x-7)=1}$



Can't explain -don't answer ​

Answer 1

Answer:

Value of x = 12

Step-by-step explanation:

Given :- log₅(x-7) = 1

Use property of logarithm logₐx = y

means aʸ = x

• ∴ (x-7) = 5¹

• x - 7 = 5

• x = 12 Answer

Answer 2

Basis of Logarithm

Let's talk about

"What is a logarithm?"

In the attachment is an exponent function. It grows exponentially and is used to show very big numbers. If we know the exponent, it is no problem when the number is very big.

Now, how are we going to find the exponent of other numbers? By the logarithm. The logarithm is invented to find the exponent.

For example:-

$2=\log_{10}100$ (Logarithm), $10^2=100$ (Exponential)

• 2 is the exponent.
• 10 is the base.
• 100 is the power.

________________________________________

Solution

$\log_{5}(x-7)=1$

Here,

• 1 is the exponent.
• 5 is the base.
• $x-7$ is the power.

So,

$\rightarrow5^{1}=x-7$

$\rightarrow x-7=5$

$\rightarrow x=12$

________________________________________

More Information

As the logarithm and the exponent are related to each other, there are some important facts about the logarithm. Here are some of them.

Example: $2\times 3=6$

If we express this using logarithm of base 5,

$\rightarrow5^{\log_{5}2}\times 5^{\log_{5}3}=5^{\log_{5}6}$

We learned that product of numbers is a power sum.

$\rightarrow 5^{\log_{5}2+\log_{5}3}=5^{\log_{5}6}$

Now we can compare the exponent.

$\rightarrow\log_{5}2+\log_{5}3=\log_{5}6$ (Log sum)

There are more similar facts about logarithm, as logarithm is related to the exponent, such as log difference and base/power change.