find the exact value of the expression

1.logbase8(2)
2.logbase10(1.25)+logbase10(80)
how do you start out ? i forgot all about logarithym.s please help with step my steps

This is not calculus.

Log(base8) of 2 is what power x of 8 you must have so that 8^x = 2
2 is the cube root of 8, so the answer is 1/3.

2. logbase10(1.25)+logbase10(80)
= log(base10)(1.25*80)
= Log(base10)(100)
What is the number x such that 10^x = 100 ?

To find the exact value of the given expressions, you will need to use the properties and rules of logarithms. Let's break down each expression step by step:

1. logbase8(2)
To find this logarithm, we need to determine the power to which 8 must be raised to equal 2. In other words, we are looking for the exponent (or power) that goes in the place of an unknown "x" in the equation 8^x = 2.

To solve for x, we can rewrite the equation using the definition of logarithms: logbase8(2) = x. This equation tells us that 8 raised to the power of x equals 2.

Since 8 is not easy to work with, we can rewrite it in terms of a more manageable base. In this case, we can rewrite 8 = 2^3, since 2^3 = 8. Substituting this into the equation, we get:

logbase8(2) = logbase(2^3)(2)

By the logarithm power rule, we can rewrite the equation as:

logbase8(2) = 3 * logbase2(2)

The logarithm base 2 of 2 equals 1, so the equation simplifies to:

logbase8(2) = 3 * 1

Therefore, the exact value of logbase8(2) is 3.

2. logbase10(1.25) + logbase10(80)
To simplify this expression, we can use the logarithm product rule, which states that log(a) + log(b) = log(a * b).

Applying this rule, we have:

logbase10(1.25) + logbase10(80) = logbase10(1.25 * 80)

Multiplying 1.25 by 80, we get:

logbase10(1.25 * 80) = logbase10(100)

Since 10 raised to any power equals 100, we can rewrite the equation as:

logbase10(100) = 2

Therefore, the exact value of logbase10(1.25) + logbase10(80) is 2.