**Introduction to solving logarithms homework:**

In mathematics, the logarithm to a number to a given base is the exponent to which the base should be raised in order to produce that number. For example, the logarithm of 10000 to base 10
is 4, because 4 is the power to which ten should be raised to produce 10000: 104 = 10000, so log_{10}10000 = 4. Only positive real numbers contain real number logarithms; negative &
complex numbers have complex logarithms.

Let us see method for solving logarithms homework and some problems and propertires of logarithms homework.

The logarithm of a to the base b is written logb(a) or, if the base is implicit, as log(a). So, for a number a, a base b and an exponent y,

If a = b^{y}, then y = log_{b} (a)

The bases used often are 10 for the common logarithm, & e for the natural logarithm, & 2 for the binary logarithm.

The exercise of logarithms to make easy complicated calculations was a significant impulse in their original development. Logarithms have applications in fields as assorted as statistics, chemistry, physics, astronomy, computer science, economics, music, & engineering.

There are four basic rulers to be followed and they are given away as follows,

1) Product Rule

log_{a} xy = log_{a} x + log_{a} y

2) Quotient Rule

if= log_{a} x – log_{a} y

3) Power Rule

log_{a} xn = nlog_{a} x

4) Change of Base Rule

Log_{a}b = log_{c}b/log_{c}a

**Problem 1:**

Solve for x : log_{2}x = 6

**Solution:**

Given, log_{2}x = 6

We know that log_{b}a = c then `b^c = a`

log_{2}x = 6

2^6 = x

64 = x

x = 64.

**Answer: x =64**

**Problem 2:**

Solve for m:3^{m} = 1000

**Solution:**

Given 3^{m} = 1000

Take log on both sides,

log 3^{m} = log 1000

m log 3 = log 10^3

m ( 0.477) = 3 log 10

m(0.477) = 3 (1)

Divided by 0.477 on both sides,

m = 3 / 0.422

m = 7.1