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Chapter 10: Q. 326 (page 1055)

In the following exercises, solve each equation.

loga64=2.

Short Answer

Expert verified

The solution isa=8.

Step by step solution

01

Step 1 Given equation is,

loga64=2.

The objective is, we need to find the solution for the given equation.

The standard form of exponential equation is,x=ay.

02

Step 2 First convert the given equation into the exponential equation,

Here,y=2,a=a,x=64.

64=a2a=64a=卤8

The logarithm of negative number does not exist.

So, discard role="math" localid="1645008700858" a=-8.

So, the solution is,a=8.

03

Step 3 Let us check the answer.

Substitute a=8into the given equation.

log864=2log882=22=2

which is true.

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